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Sondow, Jonathan D.

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Author ID: sondow.jonathan-d Recent zbMATH articles by "Sondow, Jonathan D."
Published as: Sondow, Jonathan; Sondow, J.; Sondow, Jonathan D.
Homepage: http://home.earthlink.net/~jsondow/
External Links: MGP
Documents Indexed: 57 Publications since 1966
Reviewing Activity: 1 Review

Publications by Year

Citations contained in zbMATH Open

43 Publications have been cited 270 times in 188 Documents Cited by Year
Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent. Zbl 1216.11075
Guillera, Jesús; Sondow, Jonathan
54
2008
Double integrals for Euler’s constant and \(\ln \frac 4\pi\) and an analog of Hadjicostas’s formula. Zbl 1138.11356
Sondow, Jonathan
22
2005
Analytic continuation of Riemann’s zeta function and values at negative integers via Euler’s transformation of series. Zbl 0796.11033
Sondow, Jonathan
20
1994
The generalized-Euler-constant function \(\gamma (z)\) and a generalization of Somos’s quadratic recurrence constant. Zbl 1113.11017
Sondow, Jonathan; Hadjicostas, Petros
20
2007
Criteria for irrationality of Euler’s constant. Zbl 1113.11040
Sondow, Jonathan
16
2003
Nonlinear smooth representations of compact Lie groups. Zbl 0396.57003
Rothenberg, M.; Sondow, J.
12
1979
Euler’s constant, \(q\)-logarithms, and formulas of Ramanujan and Gosper. Zbl 1132.11056
Sondow, Jonathan; Zudilin, Wadim
9
2006
A faster product for \(\pi\) and a new integral for \(\ln \frac{\pi}{2}\). Zbl 1159.11328
Sondow, Jonathan
7
2005
New Vacca-type rational series for Euler’s constant \(\gamma\) and its “alternating” analog \(\ln\,\frac4\pi\). Zbl 1258.11103
Sondow, Jonathan
7
2010
Ramanujan primes and Bertrand’s postulate. Zbl 1229.11013
Sondow, Jonathan
7
2009
When is a manifold a leaf of some foliation? Zbl 0309.57012
Sondow, Jonathan D.
7
1975
Some homeomorphic sphere pairs that are combinatorially distinct. Zbl 0173.26104
Siebenmann, L.; Sondow, J.
7
1966
Infinite products with strongly \(B\)-multiplicative exponents. Zbl 1174.11006
Allouche, J.-P.; Sondow, J.
6
2008
Reducing the Erdős-Moser equation \(1^n + 2^n + \dots + k^n = (k + 1)^n\) modulo \(k\) and \(k^2\). Zbl 1233.11038
Sondow, Jonathan; MacMillan, Kieren
6
2011
A geometric proof that \(e\) is irrrational and a new measure of its irrationality. Zbl 1149.11035
Sondow, Jonathan
6
2006
Power-sum denominators. Zbl 1391.11052
Kellner, Bernd C.; Sondow, Jonathan
6
2017
Proofs of power sum and binomial coefficient congruences via Pascal’s identity. Zbl 1230.05014
MacMillan, Kieren; Sondow, Jonathan
5
2011
Divisibility of power sums and the generalized Erdős-Moser equation. Zbl 1264.11025
MacMillan, Kieren; Sondow, Jonathan
5
2012
New Wallis- and Catalan-type infinite products for \(\pi\), \(e\), and \(\sqrt{2 + \sqrt 2}\). Zbl 1216.40002
Sondow, Jonathan; Yi, Huang
5
2010
On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions. Zbl 1423.33003
Campbell, John M.; D’Aurizio, Jacopo; Sondow, Jonathan
4
2019
Ramanujan primes: bounds, runs, twins, and gaps. Zbl 1229.11014
Sondow, Jonathan; Nicholson, John W.; Noe, Tony D.
3
2011
On the congruence \(1^m + 2^m + \ldots + m^m\equiv n \bmod m\) with \(n\mid m\). Zbl 1400.11007
Grau, José María; Oller-Marcén, Antonio M.; Sondow, Jonathan
3
2015
Generalized Ramanujan primes. Zbl 1358.11095
Amersi, Nadine; Beckwith, Olivia; Miller, Steven J.; Ronan, Ryan; Sondow, Jonathan
3
2014
Zeros of the alternating zeta function on the line \(\text{Re}(s)=1\). Zbl 1187.11031
Sondow, Jonathan
3
2003
The Riemann hypothesis, simple zeros and the asymptotic convergence degree of improper Riemann sums. Zbl 0890.11025
Sondow, Jonathan
2
1998
Summation of series defined by counting blocks of digits. Zbl 1131.11009
Allouche, J.-P.; Shallit, J.; Sondow, J.
2
2007
A monotonicity property of Riemann’s xi function and a reformulation of the Riemann hypothesis. Zbl 1218.11079
Sondow, Jonathan; Dumitrescu, Cristian
2
2010
“Integrals over polytopes, multiple zeta values and polylogarithms, and Euler’s constant”. Zbl 1219.11131
Sondow, J.; Zlobin, S. A.
2
2008
Which partial sums of the Taylor series for \(e\) are convergents to \(e\)? (and a link to the primes 2, 5, 13, 37, 463). II. Zbl 1227.11031
Sondow, Jonathan; Schalm, Kyle
2
2010
Algebraic and transcendental solutions of some exponential equations. Zbl 1224.11059
Sondow, Jonathan; Marques, Diego
2
2010
Robin’s theorem, primes, and a new elementary reformulation of the Riemann hypothesis. Zbl 1235.11082
Caveney, Geoffrey; Nicolas, Jean-Louis; Sondow, Jonathan
2
2011
The denominators of power sums of arithmetic progressions. Zbl 1423.11029
Kellner, Bernd C.; Sondow, Jonathan
2
2018
Fixed points of Anosov maps of certain manifolds. Zbl 0351.58008
Sondow, Jonathan D.
1
1977
Integrals over polytopes, multiple zeta values and polylogarithms, and Euler’s constant. Zbl 1172.11028
Sondow, J.; Zlobin, S. A.
1
2008
The parbelos, a parabolic analog of the arbelos. Zbl 1291.51018
Sondow, Jonathan
1
2013
Schanuel’s conjecture and algebraic powers \(z^w\) and \(w^z\) with \(z\) and \(w\) transcendental. Zbl 1226.11075
Marques, Diego; Sondow, Jonathan
1
2010
A simple counterexample to Havil’s “reformulation” of the Riemann hypothesis. Zbl 1322.11093
Sondow, Jonathan
1
2012
Lerch quotients, Lerch primes, Fermat-Wilson quotients, and the Wieferich-non-Wilson primes \(2, 3, 14771\). Zbl 1371.11010
Sondow, Jonathan
1
2014
A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler’s constant. With an appendix by Sergey Zlobin. Zbl 1203.11053
Sondow, Jonathan
1
2009
Primary pseudoperfect numbers, arithmetic progressions, and the Erdős-Moser equation. Zbl 1391.11067
Sondow, Jonathan; MacMillan, Kieren
1
2017
Newton quadrilaterals, the associated cubic equations, and their rational solutions. Zbl 07031611
Hajja, Mowaffaq; Sondow, Jonathan
1
2019
Ramanujan, Robin, highly composite numbers, and the Riemann hypothesis. Zbl 1310.01012
Nicolas, Jean-Louis; Sondow, Jonathan
1
2014
A parametrized series representation for Apery’s constant \(\zeta(3)\). Zbl 1342.11072
Alzer, Horst; Sondow, Jonathan
1
2016
On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions. Zbl 1423.33003
Campbell, John M.; D’Aurizio, Jacopo; Sondow, Jonathan
4
2019
Newton quadrilaterals, the associated cubic equations, and their rational solutions. Zbl 07031611
Hajja, Mowaffaq; Sondow, Jonathan
1
2019
The denominators of power sums of arithmetic progressions. Zbl 1423.11029
Kellner, Bernd C.; Sondow, Jonathan
2
2018
Power-sum denominators. Zbl 1391.11052
Kellner, Bernd C.; Sondow, Jonathan
6
2017
Primary pseudoperfect numbers, arithmetic progressions, and the Erdős-Moser equation. Zbl 1391.11067
Sondow, Jonathan; MacMillan, Kieren
1
2017
A parametrized series representation for Apery’s constant \(\zeta(3)\). Zbl 1342.11072
Alzer, Horst; Sondow, Jonathan
1
2016
On the congruence \(1^m + 2^m + \ldots + m^m\equiv n \bmod m\) with \(n\mid m\). Zbl 1400.11007
Grau, José María; Oller-Marcén, Antonio M.; Sondow, Jonathan
3
2015
Generalized Ramanujan primes. Zbl 1358.11095
Amersi, Nadine; Beckwith, Olivia; Miller, Steven J.; Ronan, Ryan; Sondow, Jonathan
3
2014
Lerch quotients, Lerch primes, Fermat-Wilson quotients, and the Wieferich-non-Wilson primes \(2, 3, 14771\). Zbl 1371.11010
Sondow, Jonathan
1
2014
Ramanujan, Robin, highly composite numbers, and the Riemann hypothesis. Zbl 1310.01012
Nicolas, Jean-Louis; Sondow, Jonathan
1
2014
The parbelos, a parabolic analog of the arbelos. Zbl 1291.51018
Sondow, Jonathan
1
2013
Divisibility of power sums and the generalized Erdős-Moser equation. Zbl 1264.11025
MacMillan, Kieren; Sondow, Jonathan
5
2012
A simple counterexample to Havil’s “reformulation” of the Riemann hypothesis. Zbl 1322.11093
Sondow, Jonathan
1
2012
Reducing the Erdős-Moser equation \(1^n + 2^n + \dots + k^n = (k + 1)^n\) modulo \(k\) and \(k^2\). Zbl 1233.11038
Sondow, Jonathan; MacMillan, Kieren
6
2011
Proofs of power sum and binomial coefficient congruences via Pascal’s identity. Zbl 1230.05014
MacMillan, Kieren; Sondow, Jonathan
5
2011
Ramanujan primes: bounds, runs, twins, and gaps. Zbl 1229.11014
Sondow, Jonathan; Nicholson, John W.; Noe, Tony D.
3
2011
Robin’s theorem, primes, and a new elementary reformulation of the Riemann hypothesis. Zbl 1235.11082
Caveney, Geoffrey; Nicolas, Jean-Louis; Sondow, Jonathan
2
2011
New Vacca-type rational series for Euler’s constant \(\gamma\) and its “alternating” analog \(\ln\,\frac4\pi\). Zbl 1258.11103
Sondow, Jonathan
7
2010
New Wallis- and Catalan-type infinite products for \(\pi\), \(e\), and \(\sqrt{2 + \sqrt 2}\). Zbl 1216.40002
Sondow, Jonathan; Yi, Huang
5
2010
A monotonicity property of Riemann’s xi function and a reformulation of the Riemann hypothesis. Zbl 1218.11079
Sondow, Jonathan; Dumitrescu, Cristian
2
2010
Which partial sums of the Taylor series for \(e\) are convergents to \(e\)? (and a link to the primes 2, 5, 13, 37, 463). II. Zbl 1227.11031
Sondow, Jonathan; Schalm, Kyle
2
2010
Algebraic and transcendental solutions of some exponential equations. Zbl 1224.11059
Sondow, Jonathan; Marques, Diego
2
2010
Schanuel’s conjecture and algebraic powers \(z^w\) and \(w^z\) with \(z\) and \(w\) transcendental. Zbl 1226.11075
Marques, Diego; Sondow, Jonathan
1
2010
Ramanujan primes and Bertrand’s postulate. Zbl 1229.11013
Sondow, Jonathan
7
2009
A hypergeometric approach, via linear forms involving logarithms, to criteria for irrationality of Euler’s constant. With an appendix by Sergey Zlobin. Zbl 1203.11053
Sondow, Jonathan
1
2009
Double integrals and infinite products for some classical constants via analytic continuations of Lerch’s transcendent. Zbl 1216.11075
Guillera, Jesús; Sondow, Jonathan
54
2008
Infinite products with strongly \(B\)-multiplicative exponents. Zbl 1174.11006
Allouche, J.-P.; Sondow, J.
6
2008
“Integrals over polytopes, multiple zeta values and polylogarithms, and Euler’s constant”. Zbl 1219.11131
Sondow, J.; Zlobin, S. A.
2
2008
Integrals over polytopes, multiple zeta values and polylogarithms, and Euler’s constant. Zbl 1172.11028
Sondow, J.; Zlobin, S. A.
1
2008
The generalized-Euler-constant function \(\gamma (z)\) and a generalization of Somos’s quadratic recurrence constant. Zbl 1113.11017
Sondow, Jonathan; Hadjicostas, Petros
20
2007
Summation of series defined by counting blocks of digits. Zbl 1131.11009
Allouche, J.-P.; Shallit, J.; Sondow, J.
2
2007
Euler’s constant, \(q\)-logarithms, and formulas of Ramanujan and Gosper. Zbl 1132.11056
Sondow, Jonathan; Zudilin, Wadim
9
2006
A geometric proof that \(e\) is irrrational and a new measure of its irrationality. Zbl 1149.11035
Sondow, Jonathan
6
2006
Double integrals for Euler’s constant and \(\ln \frac 4\pi\) and an analog of Hadjicostas’s formula. Zbl 1138.11356
Sondow, Jonathan
22
2005
A faster product for \(\pi\) and a new integral for \(\ln \frac{\pi}{2}\). Zbl 1159.11328
Sondow, Jonathan
7
2005
Criteria for irrationality of Euler’s constant. Zbl 1113.11040
Sondow, Jonathan
16
2003
Zeros of the alternating zeta function on the line \(\text{Re}(s)=1\). Zbl 1187.11031
Sondow, Jonathan
3
2003
The Riemann hypothesis, simple zeros and the asymptotic convergence degree of improper Riemann sums. Zbl 0890.11025
Sondow, Jonathan
2
1998
Analytic continuation of Riemann’s zeta function and values at negative integers via Euler’s transformation of series. Zbl 0796.11033
Sondow, Jonathan
20
1994
Nonlinear smooth representations of compact Lie groups. Zbl 0396.57003
Rothenberg, M.; Sondow, J.
12
1979
Fixed points of Anosov maps of certain manifolds. Zbl 0351.58008
Sondow, Jonathan D.
1
1977
When is a manifold a leaf of some foliation? Zbl 0309.57012
Sondow, Jonathan D.
7
1975
Some homeomorphic sphere pairs that are combinatorially distinct. Zbl 0173.26104
Siebenmann, L.; Sondow, J.
7
1966
all top 5

Cited by 211 Authors

14 Sondow, Jonathan D.
7 Simsek, Yilmaz
6 Allouche, Jean-Paul Simon
6 Chen, Chaoping
5 Grau, José María
5 Kellner, Bernd C.
5 Oller-Marcén, Antonio M.
5 Sofo, Anthony
4 Adell, José Antonio
4 Lekuona, Alberto
3 Alzer, Horst
3 Axler, Christian
3 Blagouchine, Iaroslav V.
3 Campbell, John Maxwell
3 Hessami Pilehrood, Khodabakhsh
3 Hessami Pilehrood, Tatiana
3 Luca, Florian
3 Moree, Pieter
3 Mortici, Cristinel
3 Wang, Kai
2 Browder, William
2 Chen, Dirong
2 Choi, Junesang
2 Elsner, Carsten
2 Ferreira, Erasmo M.
2 Katō, Mitsuyoshi
2 Kohara, Anderson K.
2 Lagarias, Jeffrey C.
2 Lampret, Vito
2 Li, Xiumei
2 Lu, Dawei
2 Marques, Diego
2 Moll, Victor Hugo
2 Navas, Luis M.
2 Nimbran, Amrik Singh
2 Paris, Richard Bruce
2 Ruiz, Francisco J.
2 Sampedro, Juan Carlos
2 Schultz, Reinhard E.
2 Schweitzer, Paul A.
2 Sesma, Javier
2 Sha, Min
2 Shallit, Jeffrey O.
2 Siebenmann, Laurence C.
2 Srivastava, Hari Mohan
2 van Gorder, Robert Ashton
2 Varona Malumbres, Juan Luis
2 Vignat, Christophe
2 Weinberger, Shmuel
2 Xu, Aimin
2 You, Xu
2 Young, Paul Thomas
2 Zaharescu, Alexandru
2 Zlobin, S. A.
1 Abel, Ulrich
1 Acikgoz, Mehmet
1 Agarwal, Hans
1 Agarwal, Ravi P.
1 Alekseyev, Max A.
1 Alvarez Alonso, Josefina
1 Amore, Paolo
1 Anderson, Douglas Ross
1 Arredondo, John Alexander
1 Assadi, Amir H.
1 Batir, Necdet
1 Bayad, Abdelmejid
1 Bérczes, Attila
1 Berndt, Bruce Carl
1 Biane, Philippe
1 Bordellès, Olivier
1 Boyadzhiev, Khristo N.
1 Bradley, David M.
1 Brychkov, Yury A.
1 Cantwell, John C.
1 Caveney, Geoffrey
1 Chamberland, Marc
1 Charalambakis, Nicolas Ch.
1 Chatzigeorgiou, George
1 Chen, Yonggao
1 Cherman, Aleksey
1 Chikayama, Eisuke
1 Chikayama, Shori
1 Chu, Wenchang
1 Coffey, Mark William
1 Colley, Susan Jane
1 Conlon, Lawrence
1 Cristea, Valentin Gabriel
1 Damjanović, Danijela
1 D’Aurizio, Jacopo
1 Dixit, Atul
1 Dovermann, Karl Heinz
1 Estrada, Ricardo
1 Everest, Graham Robert
1 Ferretti, Federica
1 Fortuny Ayuso, Pedro
1 Fortuny, P.
1 Friedli, Fabien
1 Friedmann, Tamar
1 Fuchs, Dmitry Borisovich
1 Gambini, Alessandro
...and 111 more Authors
all top 5

Cited in 84 Serials

23 Journal of Number Theory
15 The Ramanujan Journal
10 Journal of Mathematical Analysis and Applications
9 American Mathematical Monthly
7 Bulletin of the American Mathematical Society
6 Integral Transforms and Special Functions
6 Integers
5 Transactions of the American Mathematical Society
5 International Journal of Number Theory
4 Monatshefte für Mathematik
4 Results in Mathematics
3 Mathematics of Computation
3 Functiones et Approximatio. Commentarii Mathematici
3 Inventiones Mathematicae
3 Bulletin of the American Mathematical Society. New Series
2 Discrete Applied Mathematics
2 Indian Journal of Pure & Applied Mathematics
2 Mathematical Notes
2 The Mathematical Intelligencer
2 Journal of Approximation Theory
2 Mathematische Zeitschrift
2 Journal de Théorie des Nombres de Bordeaux
2 Russian Journal of Mathematical Physics
2 Journal of Inequalities and Applications
2 Journal of Integer Sequences
2 Research in the Mathematical Sciences
1 Analysis Mathematica
1 Computers & Mathematics with Applications
1 International Journal of Engineering Science
1 International Journal of Mathematical Education in Science and Technology
1 Israel Journal of Mathematics
1 Journal of Mathematical Physics
1 Periodica Mathematica Hungarica
1 Rocky Mountain Journal of Mathematics
1 Journal of Geometry and Physics
1 Beiträge zur Algebra und Geometrie
1 Advances in Mathematics
1 Annales de l’Institut Fourier
1 Annales Polonici Mathematici
1 Applied Mathematics and Computation
1 Commentationes Mathematicae Universitatis Carolinae
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Computational and Applied Mathematics
1 Journal of Soviet Mathematics
1 Kodai Mathematical Journal
1 Mathematische Nachrichten
1 Mathematica Slovaca
1 Mathematika
1 Proceedings of the American Mathematical Society
1 Real Analysis Exchange
1 Tohoku Mathematical Journal. Second Series
1 Topology and its Applications
1 Advances in Applied Mathematics
1 Ergodic Theory and Dynamical Systems
1 Information and Computation
1 Applied Mathematics Letters
1 International Journal of Mathematics
1 International Journal of Algebra and Computation
1 Elemente der Mathematik
1 Linear Algebra and its Applications
1 Expositiones Mathematicae
1 Indagationes Mathematicae. New Series
1 Journal of Mathematical Sciences (New York)
1 Abstract and Applied Analysis
1 Geometry & Topology
1 Fractional Calculus & Applied Analysis
1 Analysis (München)
1 Acta Mathematica Sinica. English Series
1 Journal of High Energy Physics
1 Mathematical Modelling and Analysis
1 Miscelánea Matemática
1 Central European Journal of Mathematics
1 Journal of Intelligent and Fuzzy Systems
1 Advances in Difference Equations
1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche
1 Scientia. Series A: Mathematical Sciences. New Series
1 Journal of Mathematical Inequalities
1 Acta Mathematica Universitatis Ostraviensis
1 Math Horizons
1 Journal of Topology and Analysis
1 Probability Surveys
1 Evolution Equations and Control Theory
1 Arnold Mathematical Journal
1 Open Mathematics

Citations by Year