# zbMATH — the first resource for mathematics

## The Ramanujan Journal

### An International Journal Devoted to the Areas of Mathematics Influenced by Ramanujan

 Short Title: Ramanujan J. Publisher: Springer US, New York, NY ISSN: 1382-4090; 1572-9303/e Online: http://link.springer.com/journal/volumesAndIssues/11139 Comments: Indexed cover-to-cover
 Documents Indexed: 1,634 Publications (since 1997) References Indexed: 1,413 Publications with 24,643 References.
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#### Latest Issues

 55, No. 3 (2021) 55, No. 2 (2021) 55, No. 1 (2021) 54, No. 3 (2021) 54, No. 2 (2021) 54, No. 1 (2021) 53, No. 3 (2020) 53, No. 2 (2020) 53, No. 1 (2020) 52, No. 3 (2020) 52, No. 2 (2020) 52, No. 1 (2020) 51, No. 3 (2020) 51, No. 2 (2020) 51, No. 1 (2020) 50, No. 3 (2019) 50, No. 2 (2019) 50, No. 1 (2019) 49, No. 3 (2019) 49, No. 2 (2019) 49, No. 1 (2019) 48, No. 3 (2019) 48, No. 2 (2019) 48, No. 1 (2019) 47, No. 3 (2018) 47, No. 2 (2018) 47, No. 1 (2018) 46, No. 3 (2018) 46, No. 2 (2018) 46, No. 1 (2018) 45, No. 3 (2018) 45, No. 2 (2018) 45, No. 1 (2018) 44, No. 3 (2017) 44, No. 2 (2017) 44, No. 1 (2017) 43, No. 3 (2017) 43, No. 2 (2017) 43, No. 1 (2017) 42, No. 3 (2017) 42, No. 2 (2017) 42, No. 1 (2017) 41, No. 1-3 (2016) 40, No. 3 (2016) 40, No. 2 (2016) 40, No. 1 (2016) 39, No. 3 (2016) 39, No. 2 (2016) 39, No. 1 (2016) 38, No. 3 (2015) 38, No. 2 (2015) 38, No. 1 (2015) 37, No. 3 (2015) 37, No. 2 (2015) 37, No. 1 (2015) 36, No. 3 (2015) 36, No. 1-2 (2015) 35, No. 3 (2014) 35, No. 2 (2014) 35, No. 1 (2014) 34, No. 3 (2014) 34, No. 2 (2014) 34, No. 1 (2014) 33, No. 3 (2014) 33, No. 2 (2014) 33, No. 1 (2014) 32, No. 3 (2013) 32, No. 2 (2013) 32, No. 1 (2013) 31, No. 3 (2013) 31, No. 1-2 (2013) 30, No. 3 (2013) 30, No. 2 (2013) 30, No. 1 (2013) 29, No. 1-3 (2012) 28, No. 3 (2012) 28, No. 2 (2012) 28, No. 1 (2012) 27, No. 3 (2012) 27, No. 2 (2012) 27, No. 1 (2012) 26, No. 3 (2011) 26, No. 2 (2011) 26, No. 1 (2011) 25, No. 3 (2011) 25, No. 2 (2011) 25, No. 1 (2011) 24, No. 3 (2011) 24, No. 2 (2011) 24, No. 1 (2011) 23, No. 1-3 (2010) 22, No. 3 (2010) 22, No. 2 (2010) 22, No. 1 (2010) 21, No. 3 (2010) 21, No. 2 (2010) 21, No. 1 (2010) 20, No. 3 (2009) 20, No. 2 (2009) 20, No. 1 (2009) ...and 57 more Volumes
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#### Authors

 31 Hirschhorn, Michael D. 17 Andrews, George Eyre 17 Xia, Ernest X. W. 15 Sárközy, András 13 Berndt, Bruce Carl 13 Chu, Wenchang 13 Kohnen, Winfried 11 Baruah, Nayandeep Deka 11 Chern, Shane 11 Lin, Bernard L. S. 11 Merca, Mircea 11 Moll, Victor Hugo 11 Zhou, Yajun 10 Alladi, Krishnaswami 10 Borwein, Jonathan Michael 10 Cooper, Shaun 10 Sellers, James Allen 10 Yao, Olivia Xiang Mei 10 Yee, Ae Ja 9 Chen, William Yong-Chuan 9 Guillera, Jesús 9 Liu, Zhi-Guo 9 Mc Laughlin, James G. 9 Nicolas, Jean-Louis 9 Zeng, Jiang 8 Choie, YoungJu 8 Elliott, Peter D. T. A. 8 Koo, Jakyung 8 Luca, Florian 7 Bringmann, Kathrin 7 Chan, Heng Huat 7 Kim, Chang Heon 7 Mauduit, Christian 7 McIntosh, Richard J. 7 Tenenbaum, Gérald 7 Vignat, Christophe 7 Zaharescu, Alexandru 6 Alkan, Emre 6 Chen, Chaoping 6 Dixit, Atul 6 Gu, Nancy Shan Shan 6 Lu, Guangshi 6 Ono, Ken 6 Pomerance, Carl Bernard 6 Suslov, Sergei K. 6 Tang, Dazhao 6 Warnaar, S. Ole 6 Zhedanov, Alexei S. 5 Amdeberhan, Tewodros 5 Berkovich, Alexander 5 Cui, Su-Ping 5 Guerzhoy, Pavel I. 5 Guo, Victor J. W. 5 Gyarmati, Katalin 5 Han, Guo-Niu 5 He, Bing 5 Kim, Byungchan 5 Kim, Myung-Hwan 5 Knopp, Marvin Isadore 5 Lu, Dawei 5 Mao, Guo-Shuai 5 Mason, Geoffrey 5 Matsuda, Kazuhide 5 O’Sullivan, Cormac 5 Shen, Lichien 5 Srivastava, Hari Mohan 5 Takeyama, Yoshihiro 5 Vinet, Luc 5 Wang, Liuquan 5 Wei, Chuanan 5 Wu, Jie 4 Ballantine, Cristina M. 4 Banks, William D. 4 Barman, Rupam 4 Basu, Ankur 4 Borwein, David 4 Bouzeffour, Fethi 4 Brown, Jim L. 4 Cai, Yingchun 4 Chan, Song Heng 4 de Azevedo Pribitkin, Wladimir 4 Dilcher, Karl 4 Dou, Donna Quan Jie 4 El Bachraoui, Mohamed 4 Elsner, Carsten 4 Espinosa, Olivier 4 Feĭgin, Boris L’vovich 4 Folsom, Amanda 4 Garvan, Frank G. 4 Gasper, George Jun 4 Granville, Andrew James 4 Griffin, James C. 4 Hegyvári, Norbert 4 Huber, Tim 4 Ismail, Mourad El-Houssieny 4 Ito, Masahiko 4 Ivić, Aleksandar P. 4 James, Kevin 4 Jimbo, Michio 4 Jouhet, Frédéric ...and 1,511 more Authors
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#### Fields

 1,289 Number theory (11-XX) 458 Special functions (33-XX) 387 Combinatorics (05-XX) 64 Functions of a complex variable (30-XX) 60 Algebraic geometry (14-XX) 51 Harmonic analysis on Euclidean spaces (42-XX) 46 Approximations and expansions (41-XX) 38 Sequences, series, summability (40-XX) 31 Real functions (26-XX) 31 Probability theory and stochastic processes (60-XX) 30 Difference and functional equations (39-XX) 26 Nonassociative rings and algebras (17-XX) 26 Group theory and generalizations (20-XX) 16 Ordinary differential equations (34-XX) 16 Numerical analysis (65-XX) 14 Integral transforms, operational calculus (44-XX) 12 Topological groups, Lie groups (22-XX) 12 Dynamical systems and ergodic theory (37-XX) 11 History and biography (01-XX) 11 Commutative algebra (13-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 7 General and overarching topics; collections (00-XX) 7 Associative rings and algebras (16-XX) 7 Convex and discrete geometry (52-XX) 7 Quantum theory (81-XX) 6 Partial differential equations (35-XX) 6 Computer science (68-XX) 5 Field theory and polynomials (12-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Functional analysis (46-XX) 5 Manifolds and cell complexes (57-XX) 4 Abstract harmonic analysis (43-XX) 4 Operator theory (47-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 $$K$$-theory (19-XX) 3 Geometry (51-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Measure and integration (28-XX) 2 Optics, electromagnetic theory (78-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

1,143 Publications have been cited 6,882 times in 4,783 Documents Cited by Year
On the Nevanlinna characteristic of $$f(z+\eta)$$ and difference equations in the complex plane. Zbl 1152.30024
Chiang, Yik-Man; Feng, Shao-Ji
2008
Partition bijections, a survey. Zbl 1103.05009
Pak, Igor
2006
Tridiagonal pairs and the quantum affine algebra $$U_q(\widehat{\text{sl}}_2)$$. Zbl 1128.16028
Ito, Tatsuro; Terwilliger, Paul
2007
Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent. Zbl 1216.11075
Guillera, Jesús; Sondow, Jonathan
2008
Divisibility of certain partition functions by powers of primes. Zbl 0907.11036
Gordon, Basil; Ono, Ken
1997
Relations between the ranks and cranks of partitions. Zbl 1039.11069
Atkin, A. O. L.; Garvan, F. G.
2003
The Arakawa-Kaneko zeta function. Zbl 1230.11106
Coppo, Marc-Antoine; Candelpergher, Bernard
2010
Arithmetic properties of partitions with even parts distinct. Zbl 1218.05018
Andrews, George E.; Hirschhorn, Michael D.; Sellers, James A.
2010
Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Zbl 1125.11315
Milne, Stephen C.
2002
Multiple $$q$$-zeta functions and multiple $$q$$-polylogarithms. Zbl 1200.11065
Zhao, Jianqiang
2007
Explicit estimates of some functions over primes. Zbl 1426.11088
Dusart, Pierre
2018
The evaluation of character Euler double sums. Zbl 1241.11108
Borwein, J. M.; Zucker, I. J.; Boersma, J.
2008
Some systems of multivariable orthogonal $$q$$-Racah polynomials. Zbl 1121.33019
Gasper, George; Rahman, Mizan
2007
Lecture hall partitions. Zbl 0909.05008
Bousquet-Mélou, Mireille; Eriksson, Kimmo
1997
On the signs of Fourier coefficients of cusp forms. Zbl 1045.11027
Knopp, Marvin; Kohnen, Winfried; Pribitkin, Wladimir
2003
Identities for the harmonic numbers and binomial coefficients. Zbl 1234.11022
Sofo, Anthony; Srivastava, H. M.
2011
Some classes of completely monotonic functions. II. Zbl 1110.26015
Alzer, Horst; Berg, Christian
2006
On Kemnitz’ conjecture concerning lattice-points in the plane. Zbl 1126.11011
Reiher, Christian
2007
Generators of some Ramanujan formulas. Zbl 1109.33029
Guillera, Jesús
2006
Congruences for $$\ell$$-regular partition functions modulo 3. Zbl 1252.11083
Furcy, David; Penniston, David
2012
The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators. Zbl 1166.17009
Capparelli, S.; Lepowsky, J.; Milas, A.
2006
Arithmetic of the 13-regular partition function modulo 3. Zbl 1252.11086
Webb, John J.
2011
Log-concavity of the partition function. Zbl 1322.05018
DeSalvo, Stephen; Pak, Igor
2015
Analogues of Ramanujan’s partition identities. Zbl 1281.11092
Xia, Ernest X. W.; Yao, Olivia X. M.
2013
Change of base in Bailey pairs. Zbl 0980.33013
Bressoud, D.; Ismail, M. E. H.; Stanton, D.
2000
Analogues of Ramanujan’s partition identities and congruences arising from his theta functions and modular equations. Zbl 1254.05023
Baruah, Nayandeep Deka; Ojah, Kanan Kumari
2012
On some integrals involving the Hurwitz zeta function. I. Zbl 1019.33001
Espinosa, Olivier; Moll, Victor H.
2002
On Borcherds products associated with lattices of prime discriminant. Zbl 1130.11317
Bruinier, Jan Hendrik; Bundschuh, Michael
2003
On modular forms arising from a differential equation of hypergeometric type. Zbl 1050.11047
Kaneko, Masanobu; Koike, Masao
2003
An elementary approach to $$6j$$-symbols (classical, quantum, rational, trigonometric, and elliptic). Zbl 1125.33015
Rosengren, Hjalmar
2007
Multiple zeta values at non-positive integers. Zbl 1002.11069
Akiyama, Shigeki; Tanigawa, Yoshio
2001
On some integrals involving the Hurwitz zeta function. II. Zbl 1156.11333
Espinosa, Olivier; Moll, Victor H.
2002
Hypergeometric identities for 10 extended Ramanujan-type series. Zbl 1142.33002
Guillera, Jesús
2008
The multiple gamma function and its application to computation of series. Zbl 1088.33014
2005
$$l$$-divisibility of $$l$$-regular partition functions. Zbl 1195.11140
Dandurand, Brian; Penniston, David
2009
Arithmetic properties of partitions with odd parts distinct. Zbl 1209.05016
Hirschhorn, Michael D.; Sellers, James A.
2010
Explicit evaluation of Euler and related sums. Zbl 1115.11052
Choi, Junesang; Srivastava, H. M.
2005
Limits of elliptic hypergeometric integrals. Zbl 1178.33021
Rains, Eric M.
2009
Spin Leonard pairs. Zbl 1118.05101
Curtin, Brian
2007
Statistical properties of friable integers. (Propriétés statistiques des entiers friables.) Zbl 1152.11040
de la Bretèche, Régis; Tenenbaum, Gérald
2005
Parity results for 9-regular partitions. Zbl 1308.11093
Xia, Ernest X. W.; Yao, Olivia X. M.
2014
New $$_{5}F_{4}$$ hypergeometric transformations, three-variable Mahler measures, and formulas for $$1/ \pi$$. Zbl 1226.11113
Rogers, Mathew D.
2009
Jagged partitions. Zbl 1079.05003
Fortin, J.-F.; Jacob, P.; Mathieu, P.
2005
Supercongruences for the Catalan-Larcombe-French numbers. Zbl 1218.11025
Jarvis, Frazer; Verrill, Helena A.
2010
A formula for a quartic integral: a survey of old proofs and some new ones. Zbl 1178.33002
Amdeberhan, Tewodros; Moll, Victor H.
2009
Congruences modulo 9 and 27 for overpartitions. Zbl 1422.11214
Xia, Ernest X. W.
2017
Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation. Zbl 1010.11020
Bauer, Mark; Bennett, Michael A.
2002
On relations for the multiple $$q$$-zeta values. Zbl 1211.11099
Okuda, Jun-ichi; Takeyama, Yoshihiro
2007
Quintic and septic Eisenstein series. Zbl 1259.11046
Cooper, Shaun; Toh, Pee Choon
2009
Inequalities and infinite product formula for Ramanujan generalized modular equation function. Zbl 1444.11058
Wang, Miao-Kun; Li, Yong-Min; Chu, Yu-Ming
2018
A new fast asymptotic series for the gamma function. Zbl 1329.33003
Mortici, Cristinel
2015
Multidimensional matrix inversions and $$A_r$$ and $$D_r$$ basic hypergeometric series. Zbl 0934.33006
Schlosser, Michael
1997
Lecture hall partitions. II. Zbl 0909.05009
Bousquet-Mélou, Mireille; Eriksson, Kimmo
1997
Values of Dirichlet $$L$$-functions, Gauss sums and trigonometric sums. Zbl 1287.11101
Alkan, Emre
2011
Eisenstein series and Ramanujan-type series for $$1 / \pi$$. Zbl 1204.33005
Baruah, Nayandeep Deka; Berndt, Bruce C.
2010
Ramanujan’s master theorem. Zbl 1258.33001
Amdeberhan, Tewodros; Espinosa, Olivier; Gonzalez, Ivan; Harrison, Marshall; Moll, Victor H.; Straub, Armin
2012
Ramanujan sums as supercharacters. Zbl 1368.11090
Fowler, Christopher F.; Garcia, Stephan Ramon; Karaali, Gizem
2014
Hypergeometric series, modular linear differential equations and vector-valued modular forms. Zbl 1418.11064
Franc, Cameron; Mason, Geoffrey
2016
An expansion formula for $$q$$-series and applications. Zbl 1044.05012
Liu, Zhi-Guo
2002
Convolution structure associated with the Jacobi-Dunkl operator on $$\mathbb R$$. Zbl 1122.44002
Salem, N. Ben; Salem, A. Ould Ahmed
2006
An extension of Vietoris’s inequalities. Zbl 1138.42002
Koumandos, Stamatis
2007
Infinite families of strange partition congruences for broken 2-diamonds. Zbl 1218.05024
2010
Partial theta functions and mock modular forms as $$q$$-hypergeometric series. Zbl 1283.11077
Bringmann, Kathrin; Folsom, Amanda; Rhoades, Robert C.
2012
On Ramanujan’s large argument formula for the gamma function. Zbl 1255.33001
Mortici, Cristinel
2011
Harmonic number identities via the Newton-Andrews method. Zbl 1306.05005
Wang, Weiping; Jia, Cangzhi
2014
$$q$$-Selberg integrals and Macdonald polynomials. Zbl 1086.33018
Warnaar, S. Ole
2005
On the Ramanujan-Göllnitz-Gordon continued fraction. Zbl 0905.11008
Chan, Heng Huat; Huang, Sen-Shan
1997
On the divisor function and the Riemann zeta-function in short intervals. Zbl 1226.11086
Ivić, Aleksandar
2009
Parity in partition identities. Zbl 1226.11107
Andrews, George E.
2010
Poly-Cauchy numbers with a $$q$$ parameter. Zbl 1270.05010
Komatsu, Takao
2013
Congruences for 9-regular partitions modulo 3. Zbl 1360.11105
Keith, William J.
2014
Ramanujan’s estimate for the gamma function via monotonicity arguments. Zbl 1217.33003
Mortici, Cristinel
2011
Highly composite numbers. Annotated by Jean-Louis Nicolas and Guy Robin. Zbl 0917.11043
Ramanujan, Srinivasa
1997
Short proofs of the elliptic beta integrals. Zbl 1118.33008
Spiridonov, V. P.
2007
A new class of identities involving Cauchy numbers, harmonic numbers and zeta values. Zbl 1276.11148
Candelpergher, Bernard; Coppo, Marc-Antoine
2012
Some arithmetic properties of short random walk integrals. Zbl 1233.60024
Borwein, Jonathan M.; Nuyens, Dirk; Straub, Armin; Wan, James
2011
Concave and convex compositions. Zbl 1325.05025
Andrews, George E.
2013
Sums involving the Hurwitz zeta function. Zbl 0989.11043
Kanemitsu, Shigeru; Kumagai, Hiroshi; Yoshimoto, Masami
2001
Sums and products from a finite set of real numbers. Zbl 0908.11008
Ford, Kevin
1998
Sums of products of Apostol-Bernoulli numbers. Zbl 1250.11026
Kim, Min-Soo; Hu, Su
2012
Precise estimates for the solution of Ramanujan’s generalized modular equation. Zbl 1456.11047
Wang, Miao-Kun; Chu, Yu-Ming; Zhang, Wen
2019
$$q$$-series and $$L$$-functions related to half-derivatives of the Andrews-Gordon identity. Zbl 1114.11039
Hikami, Kazuhiro
2006
The basic bilateral hypergeometric series and the mock theta functions. Zbl 1225.33019
Choi, Youn-Seo
2011
Combinatorial interpretations of congruences for the spt-function. Zbl 1256.05012
Andrews, George E.; Garvan, Frank G.; Liang, Jie
2012
Ramanujan-type partial theta identities and conjugate Bailey pairs. Zbl 1322.11107
Lovejoy, Jeremy
2012
Unit circle elliptic beta integrals. Zbl 1160.33309
van Diejen, J. F.; Spiridonov, V. P.
2005
The distribution of totients. Zbl 0914.11053
Ford, Kevin
1998
A class of series acceleration formulae for Catalan’s constant. Zbl 0946.11032
1999
Modular transformations of Ramanujan’s fifth and seventh order mock theta functions. Zbl 1031.11008
Gordon, Basil; McIntosh, Richard J.
2003
Askey-Wilson type functions with bound states. Zbl 1100.33004
Haine, Luc; Iliev, Plamen
2006
Askey-Wilson type integrals associated with root systems. Zbl 1114.33026
Ito, Masahiko
2006
On the rational approximation of the sum of the reciprocals of the Fermat numbers. Zbl 1271.11075
Coons, Michael
2013
Study of the multiplicative autocorrelation of the fractional part function. (Étude de l’autocorrélation multiplicative de la fonction ‘partie fractionnaire’.) Zbl 1173.11343
Báez-Duarte, Luis; Balazard, Michel; Landreau, Bernard; Saias, Eric
2005
Arithmetic properties of bipartitions with even parts distinct. Zbl 1298.05033
Lin, Bernard L. S.
2014
Some theorems on the Rogers-Ramanujan continued fraction and associated theta function identities in Ramanujan’s Lost Notebook. Zbl 0930.11025
Kang, Soon-Yi
1999
Sums of five, seven and nine squares. Zbl 1050.11044
Cooper, Shaun
2002
The Bailey transform and false theta functions. Zbl 1116.33017
Andrews, George E.; Warnaar, S. Ole
2007
Some new proofs of modular relations for the Göllnitz-Gordon functions. Zbl 1181.11024
Baruah, Nayandeep Deka; Bora, Jonali; Saikia, Nipen
2008
Sporadic sequences, modular forms and new series for $$1/\pi$$. Zbl 1336.11031
Cooper, Shaun
2012
On three third order mock theta functions and Hecke-type double sums. Zbl 1284.11075
Mortenson, Eric
2013
An analog of the Dougall formula and of the de Branges-Wilson integral. Zbl 1467.33009
Neretin, Yury A.
2021
Asymptotics of Nahm sums at roots of unity. Zbl 07344932
Garoufalidis, Stavros; Zagier, Don
2021
The 5-dissections of two infinite product expansions. Zbl 1466.33012
Dou, Donna Q. J.; Xiao, Jiejuan
2021
On the zeros of certain composite polynomials and an operator preserving inequalities. Zbl 1462.30013
Rather, N. A.; Dar, Ishfaq; Gulzar, Suhail
2021
On Siegel invariants of certain CM-fields. Zbl 07344955
Koo, Ja Kyung; Robert, Gilles; Shin, Dong Hwa; Yoon, Dong Sung
2021
Asymptotic equidistribution and convexity for partition ranks. Zbl 07344962
Males, Joshua
2021
Explicit congruences modulo 2048 for overpartitions. Zbl 07345298
Xue, Fanggang; Yao, Olivia X. M.
2021
Generalized Bessel functions of dihedral-type: expression as a series of confluent Horn functions and Laplace-type integral representation. Zbl 1467.33005
Deleaval, L.; Demni, N.
2021
$$q$$-analogues of three Ramanujan-type formulas for $$1/\pi$$. Zbl 07189548
Guo, Victor J. W.
2020
The q-Heun operator of big q-Jacobi type and the q-Heun algebra. Zbl 1444.39007
Baseilhac, Pascal; Vinet, Luc; Zhedanov, Alexei
2020
$$q$$-analogues of two “divergent” Ramanujan-type supercongruences. Zbl 1455.11036
Guo, Victor J. W.
2020
Little and big $$q$$-Jacobi polynomials and the Askey-Wilson algebra. Zbl 1436.81070
Baseilhac, Pascal; Martin, Xavier; Vinet, Luc; Zhedanov, Alexei
2020
Partition implications of a three-parameter $$q$$-series identity. Zbl 1445.11114
Dixit, Atul; Maji, Bibekananda
2020
Factorization theorems for generalized Lambert series and applications. Zbl 1458.11008
Merca, Mircea; Schmidt, Maxie D.
2020
Several $$q$$-series related to Ramanujan’s theta functions. Zbl 1467.33013
Tang, Dazhao; Xia, Ernest. X. W.
2020
On the non-vanishing of $$L$$-functions associated to cusp forms of half-integral weight. Zbl 1439.11123
Žunar, Sonja
2020
Universal sums of generalized pentagonal numbers. Zbl 1458.11061
Ju, Jangwon
2020
The Taylor coefficients of the Jacobi theta constant $$\theta_3$$. Zbl 1460.11053
Romik, Dan
2020
A method for proving Ramanujan’s series for $$1/\pi$$. Zbl 1440.33019
Guillera, Jesús
2020
Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients. Zbl 1444.33005
Wang, Xiaoyuan; Chu, Wenchang
2020
A general method for proving the non-trivial linear homogeneous partition inequalities. Zbl 1434.05014
Merca, Mircea; Katriel, Jacob
2020
Proofs of some conjectures of Chan and Wang on congruences for $$(q;q)_\infty^{\frac{a}{b}}$$. Zbl 07345236
Xia, Ernest X. W.; Zhu, Haiyang
2020
Note on a theorem of Farkas and Kra. Zbl 07345239
Matsuda, Kazuhide
2020
Fourier expansions at cusps. Zbl 07345243
Brunault, François; Neururer, Michael
2020
Some results on vanishing coefficients in infinite product expansions. Zbl 07345286
Baruah, Nayandeep Deka; Kaur, Mandeep
2020
Petersson scalar products and $$L$$-functions arising from modular forms. Zbl 07189543
Tsuyumine, Shigeaki
2020
Derivations on the algebra of multiple harmonic $$q$$-series and their applications. Zbl 1437.05026
Takeyama, Yoshihiro
2020
Quadratic ideals and Rogers-Ramanujan recursions. Zbl 07189545
Bai, Yuzhe; Gorsky, Eugene; Kivinen, Oscar
2020
Theta operator on Hermitian modular forms over the Eisenstein field. Zbl 1460.11061
Nagaoka, Shoyu; Takemori, Sho
2020
On a Diophantine inequality involving prime numbers. Zbl 1444.11051
Li, Sanhua; Cai, Yingchun
2020
Asymptotic formulas related to the $$M_2$$-rank of partitions without repeated odd parts. Zbl 1445.11117
Jennings-Shaffer, Chris; Reihill, Dillon
2020
Multiple zeta values for classical special functions. Zbl 1439.11224
Wakhare, Tanay; Vignat, Christophe
2020
Extended arithmetic functions. Zbl 1444.11011
Bouzeffour, Fethi; Jedidi, Wissem; Garayev, Mubariz
2020
Some properties and applications of non-trivial divisor functions. Zbl 1453.11005
Hill, S. L.; Huxley, M. N.; Lettington, M. C.; Schmidt, K. M.
2020
Bisected theta series, least $$r$$-gaps in partitions, and polygonal numbers. Zbl 1439.05023
Ballantine, Cristina; Merca, Mircea
2020
Extension of results of Kostant and Han. Zbl 1442.05018
Heim, Bernhard; Neuhauser, Markus
2020
When is the Bloch-Okounkov $$q$$-bracket modular? Zbl 1443.05014
van Ittersum, Jan-Willem M.
2020
Identities of cycle integrals of weak Maass forms. Zbl 1456.11049
Alfes-Neumann, Claudia; Schwagenscheidt, Markus
2020
Linear independence of harmonic numbers over the field of algebraic numbers. Zbl 1441.11180
Chatterjee, Tapas; Dhillon, Sonika
2020
Cubic partitions modulo powers of 5. Zbl 1450.11109
Hirschhorn, Michael D.
2020
Diophantine approximation with one prime, two squares of primes and powers of two. Zbl 1452.11035
Liu, Huafeng
2020
Proofs of some conjectures of Chan on Appell-Lerch sums. Zbl 1450.11107
Baruah, Nayandeep Deka; Begum, Nilufar Mana
2020
Modular equations for congruence subgroups of genus zero. Zbl 1458.11067
Cho, Bumkyu
2020
Diophantine inequality by unlike powers of primes. Zbl 07176796
Zhu, Li
2020
Nonvanishing of derivatives of Hecke $$L$$-functions associated to cusp forms inside the critical strip. Zbl 07176797
Kohnen, Winfried; Sengupta, Jyoti; Weigel, Miriam
2020
$$M_2$$-ranks of overpartitions modulo 6 and 10. Zbl 1440.11192
Zhang, Helen W. J.
2020
Precise estimates for the solution of Ramanujan’s generalized modular equation. Zbl 1456.11047
Wang, Miao-Kun; Chu, Yu-Ming; Zhang, Wen
2019
$$q$$-analogues of the (E.2) and (F.2) supercongruences of van Hamme. Zbl 07096579
Guo, Victor J. W.
2019
Fourier coefficients of powers of the Dedekind eta function. Zbl 1460.11049
Heim, Bernhard; Neuhauser, Markus; Rupp, Florian
2019
Sharp inequalities for the generalized elliptic integrals of the first kind. Zbl 1408.33010
Yang, Zhen-Hang; Tian, Jingfeng
2019
Two remarkable $$q$$-series expansions. Zbl 1460.11059
Hirschhorn, Michael D.
2019
Functional inequalities for the Fox-Wright functions. Zbl 1431.33007
Mehrez, Khaled; Sitnik, Sergei M.
2019
On cyclotomic factors of polynomials related to modular forms. Zbl 1450.11041
Heim, Bernhard; Luca, Florian; Neuhauser, Markus
2019
Proof of Sun’s conjectures on super congruences and the divisibility of certain binomial sums. Zbl 1428.11040
Mao, Guo-Shuai; Zhang, Tao
2019
Euler’s partition theorem for all moduli and new companions to Rogers-Ramanujan-Andrews-Gordon identities. Zbl 07096581
Xiong, Xinhua; Keith, William J.
2019
Some identities associated with mock theta functions $$\omega (q)$$ and $$\nu (q)$$. Zbl 1419.05022
Andrews, George E.; Yee, Ae Ja
2019
Kloosterman sums and Fourier coefficients of Eisenstein series. Zbl 1436.11102
Kıral, Eren Mehmet; Young, Matthew P.
2019
On second and eighth order mock theta functions. Zbl 1445.33027
Cui, Su-Ping; Gu, Nancy S. S.; Hao, Li-Jun
2019
New proofs of Ramanujan’s identities on false theta functions. Zbl 1430.33006
Wang, Liuquan
2019
Klyachko periods for Zelevinsky modules. Zbl 07096580
Offen, Omer; Sayag, Eitan
2019
Generalizations of some conjectures of Sun on the relations between $$N(a,b,c,d;n)$$ and $$T(a,b,c,d;n)$$. Zbl 1455.11060
Yao, Olivia X. M.
2019
Solutions of KZ differential equations modulo $$p$$. Zbl 1416.81080
2019
Correction to: “Almost periodic functions in terms of Bohr’s equivalence relation”. Zbl 1419.30015
Sepulcre, J. M.; Vidal, T.
2019
The partition function $$p(n)$$ in terms of the classical Möbius function. Zbl 1464.11008
Merca, Mircea; Schmidt, Maxie D.
2019
More infinite products: Thue-Morse and the gamma function. Zbl 1466.11002
Allouche, J.-P.; Riasat, S.; Shallit, J.
2019
New congruences involving products of two binomial coefficients. Zbl 1450.11014
Mao, Guo-Shuai; Sun, Zhi-Wei
2019
Uniform convergence of basic Fourier-Bessel series on a $$q$$-linear grid. Zbl 1420.42006
Abreu, L. D.; Álvarez-Nodarse, R.; Cardoso, J. L.
2019
Kala, Vítězslav; Svoboda, Josef
2019
The graded ring of modular forms on the Cayley half-space of degree two. Zbl 1444.11092
Dieckmann, C.; Krieg, A.; Woitalla, M.
2019
Topological strings, quiver varieties, and Rogers-Ramanujan identities. Zbl 1440.14261
Zhu, Shengmao
2019
On unequal powers of primes and powers of 2. Zbl 07132656
Lü, Xiaodong
2019
On mock theta functions and weight-attached Frobenius partitions. Zbl 1428.05027
Sharma, S.; Rana, M.
2019
Combinatorial proof of an identity of Andrews and Yee. Zbl 1418.05021
Chern, Shane
2019
Poincaré square series of small weight. Zbl 1459.11112
Williams, Brandon
2019
Congruences for the coefficients of the mock theta function $$\beta (q)$$. Zbl 1446.11191
Zhang, Wenlong; Shi, Ji
2019
Sharp bounds for the $$q$$-gamma function in terms of the Lambert $$W$$ function. Zbl 1431.33018
Salem, Ahmed
2019
$$Q$$-total positivity and strong $$q$$-log-convexity for some generalized triangular arrays. Zbl 1416.05043
Ahmia, Moussa; Belbachir, Hacène
2019
$$r$$-log-concavity of partition functions. Zbl 1407.05016
Hou, Qing-Hu; Zhang, Zuo-Ru
2019
Evaluation of Gaussian hypergeometric series using Huff’s models of elliptic curves. Zbl 07055390
2019
Finiteness of irreducible holomorphic eta quotients of a given level. Zbl 1444.11062
Bhattacharya, Soumya
2019
Finite generating functions for the sum-of-digits sequence. Zbl 1464.11016
Vignat, Christophe; Wakhare, Tanay
2019
A control theorem for $$p$$-adic automorphic forms and Teitelbaum’s $$\mathcal{L}$$-invariant. Zbl 07132652
Gräf, Peter Mathias
2019
Some new modular equations in Ramanujan’s alternate theory of signature 3. Zbl 1431.11061
Saikia, Nipen; Chetry, Jubaraj
2019
Natural exact covering systems and the reversion of the Möbius series. Zbl 1427.05022
Goulden, I. P.; Granville, Andrew; Richmond, L. Bruce; Shallit, Jeffrey
2019
Periodic points of algebraic functions and Deuring’s class number formula. Zbl 1461.14033
Morton, Patrick
2019
Evaluating theta derivatives with rational characteristics. Zbl 1428.14079
Zemel, Shaul
2019
On some $$q$$-versions of the Ramanujan master theorem. Zbl 1437.33016
Fitouhi, Ahmed; Brahim, Kamel; Bettaibi, Néji
2019
Closed form expressions for Appell polynomials. Zbl 1459.11055
2019
Bohr’s equivalence relation in the space of Besicovitch almost periodic functions. Zbl 1420.42004
Sepulcre, J. M.; Vidal, T.
2019
Angular changes of Fourier coefficients at primes. Zbl 1456.11055
2019
On the harmonic continued fractions. Zbl 1464.11014
Bunder, Martin; Nickolas, Peter; Tonien, Joseph
2019
Leading terms of relations for standard modules of the affine Lie algebras $$C_n^{(1)}$$. Zbl 1462.17028
Primc, Mirko; Šikić, Tomislav
2019
Supnorm of an eigenfunction of finitely many Hecke operators. Zbl 1452.11049
Jana, Subhajit
2019
On exponential and trigonometric functions on nonuniform lattices. Zbl 1431.33019
Kenfack Nangho, M.; Foupouagnigni, M.; Koepf, W.
2019
Contiguous relations, Laplace’s methods, and continued fractions for $${}_3F_2(1)$$. Zbl 1416.33011
Ebisu, Akihito; Iwasaki, Katsunori
2019
Multiple zeta values and ideles. Zbl 1451.11095
Horozov, I.
2019
Erratum/addendum to: “Kontsevich-Zagier integrals for automorphic Green’s functions. II”. Zbl 07067662
Zhou, Yajun
2019
On partitions classified by smallest missing part. Zbl 1467.11089
Shen, Yuefei
2019
On a result of Fel’dman on linear forms in the values of some $$E$$-functions. Zbl 1429.11123
Väänänen, Keijo
2019
Analytic and arithmetic properties of the $$(\Gamma ,\chi )$$-automorphic reproducing kernel function and associated Hermite-Gauss series. Zbl 1444.30019
El Fardi, A.; Ghanmi, A.; Imlal, L.; Souid El Ainin, M.
2019
...and 1043 more Documents
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#### Cited by 3,673 Authors

 40 Xia, Ernest X. W. 37 Bringmann, Kathrin 35 Terwilliger, Paul M. 34 Guo, Victor J. W. 33 Chen, Zongxuan 33 Chu, Wenchang 32 Moll, Victor Hugo 32 Sofo, Anthony 31 Luca, Florian 30 Chu, Yuming 28 Andrews, George Eyre 28 Chen, Chaoping 28 Srivastava, Hari Mohan 28 Yao, Olivia Xiang Mei 26 Cooper, Shaun 26 Kim, Byungchan 26 Lovejoy, Jeremy 26 Zudilin, Wadim 25 Chen, William Yong-Chuan 24 Barman, Rupam 24 Baruah, Nayandeep Deka 24 Mahadeva Naika, Megadahalli Sidda 24 Merca, Mircea 24 Warnaar, S. Ole 24 Xu, Ce 23 Chern, Shane 23 Komatsu, Takao 22 Choi, Junesang 22 Saikia, Nipen 22 Spiridonov, Vyacheslav Pavlovich 22 Xu, Hongyan 21 Alzer, Horst 21 Borwein, Jonathan Michael 21 Ono, Ken 21 Schlosser, Michael J. 20 Ito, Masahiko 20 Wang, Liuquan 20 Yang, Zhenhang 20 Yee, Ae Ja 19 Lin, Bernard L. S. 19 Zeng, Jiang 18 Chan, Heng Huat 18 Dixit, Atul 18 Liu, Zhi-Guo 18 Mansour, Toufik 18 Osburn, Robert 18 Tang, Dazhao 17 Berkovich, Alexander 17 Han, Guo-Niu 17 Jennings-Shaffer, Chris 16 Alkan, Emre 16 Ismail, Mourad El-Houssieny 16 Sellers, James Allen 16 Shparlinski, Igor E. 16 Vignat, Christophe 15 Berndt, Bruce Carl 15 Garvan, Frank G. 15 Li, Sheng 15 Nomura, Kazumasa 15 Straub, Armin 15 Vinet, Luc 15 Yang, Lianzhong 15 Yi, Hongxun 14 Guillera, Jesús 14 Kohnen, Winfried 14 Koo, Jakyung 14 Korhonen, Risto 14 Liu, Kai 14 Ntouyas, Sotiris K. 14 Simsek, Yilmaz 14 Tariboon, Jessada 14 Toh, Pee Choon 14 Wakayama, Masato 14 Wei, Chuanan 13 Alladi, Krishnaswami 13 Chan, Song Heng 13 Gu, Nancy Shan Shan 13 Ito, Tatsuro 13 Koumandos, Stamatis 13 Li, Xiaomin 13 Mao, Renrong 13 Mc Laughlin, James G. 13 Rhoades, Robert C. 13 Sills, Andrew V. 13 Ye, Dongxi 12 Adiga, Chandrashekar 12 Bailey, David Harold 12 Chen, Baoqin 12 Corteel, Sylvie 12 Heim, Bernhard Ernst 12 Hirschhorn, Michael D. 12 Laurinčikas, Antanas 12 Mahlburg, Karl 12 Park, Yoon Kyung 12 Pollack, Paul 12 Qi, Xiaoguang 12 Wang, Xiaoxia 12 Zhedanov, Alexei S. 12 Zhou, Yajun 11 Amdeberhan, Tewodros ...and 3,573 more Authors
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#### Cited in 416 Journals

 616 The Ramanujan Journal 354 Journal of Number Theory 223 International Journal of Number Theory 174 Journal of Mathematical Analysis and Applications 111 Proceedings of the American Mathematical Society 91 Advances in Mathematics 76 Advances in Difference Equations 75 Journal of Combinatorial Theory. Series A 70 Research in Number Theory 66 Advances in Applied Mathematics 64 Annals of Combinatorics 62 Discrete Mathematics 61 Integral Transforms and Special Functions 58 Transactions of the American Mathematical Society 54 Integers 50 Applied Mathematics and Computation 48 Bulletin of the Australian Mathematical Society 48 Mathematics of Computation 47 Linear Algebra and its Applications 45 Functiones et Approximatio. Commentarii Mathematici 42 Journal of Difference Equations and Applications 41 Journal de Théorie des Nombres de Bordeaux 39 Results in Mathematics 39 Journal of High Energy Physics 38 Rocky Mountain Journal of Mathematics 37 Acta Arithmetica 34 Journal of Approximation Theory 33 European Journal of Combinatorics 33 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 32 Monatshefte für Mathematik 32 Journal of Inequalities and Applications 32 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 30 Journal of Algebra 30 Abstract and Applied Analysis 29 Journal of Mathematical Physics 28 Archiv der Mathematik 28 Mathematische Zeitschrift 28 Mediterranean Journal of Mathematics 28 Research in the Mathematical Sciences 27 Letters in Mathematical Physics 26 Indagationes Mathematicae. New Series 23 Nuclear Physics. B 23 Comptes Rendus. Mathématique. Académie des Sciences, Paris 22 Acta Mathematica Sinica. English Series 22 Open Mathematics 21 Journal of Computational and Applied Mathematics 21 Mathematische Annalen 21 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 20 Journal of Symbolic Computation 19 Communications in Mathematical Physics 19 Mathematical Proceedings of the Cambridge Philosophical Society 19 Computational Methods and Function Theory 18 Duke Mathematical Journal 18 Journal of the Australian Mathematical Society 17 Communications in Algebra 17 Forum Mathematicum 16 American Mathematical Monthly 15 Lithuanian Mathematical Journal 15 Compositio Mathematica 15 Bulletin of the Korean Mathematical Society 15 Acta Mathematica Hungarica 15 Journal of Mathematical Inequalities 14 Indian Journal of Pure & Applied Mathematics 14 Journal für die Reine und Angewandte Mathematik 14 Manuscripta Mathematica 14 Mathematika 14 Constructive Approximation 14 Journal of Mathematical Sciences (New York) 14 Finite Fields and their Applications 14 Journal of Classical Analysis 13 Periodica Mathematica Hungarica 13 Journal of Pure and Applied Algebra 13 Mathematics 12 Israel Journal of Mathematics 12 Mathematical Notes 12 Ukrainian Mathematical Journal 12 Quaestiones Mathematicae 12 Journal of Algebraic Combinatorics 12 Journal of Integer Sequences 12 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 12 Journal of Mathematics 11 Annales de l’Institut Fourier 11 Proceedings of the Japan Academy. Series A 11 Turkish Journal of Mathematics 11 Séminaire Lotharingien de Combinatoire 11 Journal of Function Spaces 10 Experimental Mathematics 10 Afrika Matematika 9 Inventiones Mathematicae 9 Proceedings of the Edinburgh Mathematical Society. Series II 9 Theoretical Computer Science 9 Journal of the Ramanujan Mathematical Society 9 Aequationes Mathematicae 9 The Electronic Journal of Combinatorics 9 Selecta Mathematica. New Series 9 Central European Journal of Mathematics 9 Proceedings of the Steklov Institute of Mathematics 9 Science China. Mathematics 8 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 8 Czechoslovak Mathematical Journal ...and 316 more Journals
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#### Cited in 60 Fields

 3,090 Number theory (11-XX) 1,266 Special functions (33-XX) 1,128 Combinatorics (05-XX) 420 Functions of a complex variable (30-XX) 263 Difference and functional equations (39-XX) 185 Real functions (26-XX) 167 Nonassociative rings and algebras (17-XX) 163 Algebraic geometry (14-XX) 158 Quantum theory (81-XX) 139 Harmonic analysis on Euclidean spaces (42-XX) 131 Approximations and expansions (41-XX) 129 Group theory and generalizations (20-XX) 111 Ordinary differential equations (34-XX) 102 Linear and multilinear algebra; matrix theory (15-XX) 91 Numerical analysis (65-XX) 89 Probability theory and stochastic processes (60-XX) 84 Sequences, series, summability (40-XX) 54 Computer science (68-XX) 52 Dynamical systems and ergodic theory (37-XX) 49 Associative rings and algebras (16-XX) 49 Topological groups, Lie groups (22-XX) 47 Statistical mechanics, structure of matter (82-XX) 44 Integral transforms, operational calculus (44-XX) 39 Manifolds and cell complexes (57-XX) 35 Partial differential equations (35-XX) 34 Operator theory (47-XX) 32 Commutative algebra (13-XX) 30 Field theory and polynomials (12-XX) 30 Several complex variables and analytic spaces (32-XX) 29 Convex and discrete geometry (52-XX) 28 Functional analysis (46-XX) 28 Information and communication theory, circuits (94-XX) 25 Global analysis, analysis on manifolds (58-XX) 22 Abstract harmonic analysis (43-XX) 17 Geometry (51-XX) 16 History and biography (01-XX) 16 Relativity and gravitational theory (83-XX) 14 Differential geometry (53-XX) 12 Measure and integration (28-XX) 9 Order, lattices, ordered algebraic structures (06-XX) 8 Mathematical logic and foundations (03-XX) 8 Statistics (62-XX) 6 $$K$$-theory (19-XX) 6 Mechanics of particles and systems (70-XX) 5 General and overarching topics; collections (00-XX) 5 Integral equations (45-XX) 5 Operations research, mathematical programming (90-XX) 4 Category theory; homological algebra (18-XX) 4 Mechanics of deformable solids (74-XX) 4 Optics, electromagnetic theory (78-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Potential theory (31-XX) 3 Algebraic topology (55-XX) 3 Fluid mechanics (76-XX) 3 Systems theory; control (93-XX) 2 Biology and other natural sciences (92-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)