Mao, Guo-Shuai; Yang, Jun-Jun Supercongruences involving Apéry-like sequences \(\{m^nG_n(x)\}\) and \(\{m^nV_n(x)\}\). (English) Zbl 07773832 Period. Math. Hung. 87, No. 2, 303-314 (2023). MSC: 11A07 05A10 11B65 11B68 PDFBibTeX XMLCite \textit{G.-S. Mao} and \textit{J.-J. Yang}, Period. Math. Hung. 87, No. 2, 303--314 (2023; Zbl 07773832) Full Text: DOI
Xia, Wei; Sun, Zhi-Wei On congruences involving Apéry numbers. (English) Zbl 1520.11031 Proc. Am. Math. Soc. 151, No. 8, 3305-3315 (2023). MSC: 11B65 11A07 05A10 11B39 PDFBibTeX XMLCite \textit{W. Xia} and \textit{Z.-W. Sun}, Proc. Am. Math. Soc. 151, No. 8, 3305--3315 (2023; Zbl 1520.11031) Full Text: DOI arXiv
Mao, Guo-Shuai; Li, Danrui; Ma, Xinmin On some congruences involving Apéry-like numbers \(S_n\). (English) Zbl 1516.11005 J. Difference Equ. Appl. 29, No. 2, 181-197 (2023). MSC: 11A07 11B65 11B68 05A10 PDFBibTeX XMLCite \textit{G.-S. Mao} et al., J. Difference Equ. Appl. 29, No. 2, 181--197 (2023; Zbl 1516.11005) Full Text: DOI
Mao, Guo-Shuai; ZhaoSong, An-Bang On three conjectural congruences of Z.-H. Sun involving Apéry and Apéry-like numbers. (English) Zbl 1516.11007 Monatsh. Math. 201, No. 1, 197-216 (2023). MSC: 11A07 11B65 11B68 05A10 PDFBibTeX XMLCite \textit{G.-S. Mao} and \textit{A.-B. ZhaoSong}, Monatsh. Math. 201, No. 1, 197--216 (2023; Zbl 1516.11007) Full Text: DOI
Wang, Yujie; Li, Ying; Xu, Ce Evaluations of some Euler-Apéry-type series. (English) Zbl 1510.11139 Indian J. Pure Appl. Math. 53, No. 4, 849-864 (2022). Reviewer: Sami Omar (Sukhair) MSC: 11M32 05A15 05A10 11B65 PDFBibTeX XMLCite \textit{Y. Wang} et al., Indian J. Pure Appl. Math. 53, No. 4, 849--864 (2022; Zbl 1510.11139) Full Text: DOI
Zhang, Yong Some conjectural supercongruences related to Bernoulli and Euler numbers. (English) Zbl 1497.11013 Rocky Mt. J. Math. 52, No. 3, 1105-1126 (2022). MSC: 11A07 11B65 11B68 PDFBibTeX XMLCite \textit{Y. Zhang}, Rocky Mt. J. Math. 52, No. 3, 1105--1126 (2022; Zbl 1497.11013) Full Text: DOI Link
Mao, Guo-Shuai; Li, Danrui Proof of some conjectural congruences modulo \(p^3\). (English) Zbl 1498.11013 J. Difference Equ. Appl. 28, No. 4, 496-509 (2022). Reviewer: Zhihong Sun (Huaian) MSC: 11A07 05A19 11B65 11B68 11B83 PDFBibTeX XMLCite \textit{G.-S. Mao} and \textit{D. Li}, J. Difference Equ. Appl. 28, No. 4, 496--509 (2022; Zbl 1498.11013) Full Text: DOI
Zhang, Yong Three supercongruences for Apéry numbers and Franel numbers. (English) Zbl 1488.11005 Publ. Math. Debr. 98, No. 3-4, 493-511 (2021). MSC: 11A07 11B65 05A10 11B39 11B75 PDFBibTeX XMLCite \textit{Y. Zhang}, Publ. Math. Debr. 98, No. 3--4, 493--511 (2021; Zbl 1488.11005) Full Text: DOI arXiv
Tauraso, Roberto A bivariate generating function for zeta values and related supercongruences. (English) Zbl 1465.11033 J. Difference Equ. Appl. 26, No. 11-12, 1526-1537 (2020). MSC: 11A07 05A19 11B65 11M06 PDFBibTeX XMLCite \textit{R. Tauraso}, J. Difference Equ. Appl. 26, No. 11--12, 1526--1537 (2020; Zbl 1465.11033) Full Text: DOI arXiv
Mao, Guo-Shuai On two congruences involving Apéry and Franel numbers. (English) Zbl 1461.11007 Result. Math. 75, No. 4, Paper No. 159, 11 p. (2020). MSC: 11A07 05A10 11B65 PDFBibTeX XMLCite \textit{G.-S. Mao}, Result. Math. 75, No. 4, Paper No. 159, 11 p. (2020; Zbl 1461.11007) Full Text: DOI arXiv
Sun, Zhi-Hong Congruences involving binomial coefficients and Apéry-like numbers. (English) Zbl 1474.11002 Publ. Math. Debr. 96, No. 3-4, 315-346 (2020). MSC: 11A07 11B65 11B68 11E25 PDFBibTeX XMLCite \textit{Z.-H. Sun}, Publ. Math. Debr. 96, No. 3--4, 315--346 (2020; Zbl 1474.11002) Full Text: DOI arXiv
Wang, Chen Two congruences concerning Apéry numbers conjectured by Z.-W. Sun. (English) Zbl 1461.11039 Electron. Res. Arch. 28, No. 2, 1063-1075 (2020). MSC: 11B65 11B68 05A10 11A07 PDFBibTeX XMLCite \textit{C. Wang}, Electron. Res. Arch. 28, No. 2, 1063--1075 (2020; Zbl 1461.11039) Full Text: DOI arXiv
Cao, Hui-Qin; Matiyasevich, Yuri; Sun, Zhi-Wei Congruences for Apéry numbers \(\beta_n = \sum_{k = 0}^n \binom{n}{k}^2 \binom{n + k}{k}\). (English) Zbl 1471.11089 Int. J. Number Theory 16, No. 5, 981-1003 (2020). MSC: 11B65 11A07 11B68 11B75 PDFBibTeX XMLCite \textit{H.-Q. Cao} et al., Int. J. Number Theory 16, No. 5, 981--1003 (2020; Zbl 1471.11089) Full Text: DOI arXiv
Liu, Ji-Cai On a sum of Apéry-like numbers arising from spectral zeta functions. (English) Zbl 1457.11009 Colloq. Math. 160, No. 1, 1-6 (2020). Reviewer: Enzo Bonacci (Latina) MSC: 11A07 05A19 11M41 11M36 11B65 PDFBibTeX XMLCite \textit{J.-C. Liu}, Colloq. Math. 160, No. 1, 1--6 (2020; Zbl 1457.11009) Full Text: DOI
Mao, Guo-Shuai; Wang, Jie On some congruences involving Domb numbers and harmonic numbers. (English) Zbl 1433.11017 Int. J. Number Theory 15, No. 10, 2179-2200 (2019). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 11B65 11B75 11A07 PDFBibTeX XMLCite \textit{G.-S. Mao} and \textit{J. Wang}, Int. J. Number Theory 15, No. 10, 2179--2200 (2019; Zbl 1433.11017) Full Text: DOI
Gorodetsky, Ofir \(q\)-congruences, with applications to supercongruences and the cyclic sieving phenomenon. (English) Zbl 1423.11043 Int. J. Number Theory 15, No. 9, 1919-1968 (2019). MSC: 11B65 05A30 11A07 11B83 PDFBibTeX XMLCite \textit{O. Gorodetsky}, Int. J. Number Theory 15, No. 9, 1919--1968 (2019; Zbl 1423.11043) Full Text: DOI arXiv
Liu, Ji-Cai; Wang, Chen Congruences for the \((p-1)\)th Apéry number. (English) Zbl 1479.11009 Bull. Aust. Math. Soc. 99, No. 3, 362-368 (2019). Reviewer: Zhihong Sun (Huaian) MSC: 11A07 11B65 11B68 PDFBibTeX XMLCite \textit{J.-C. Liu} and \textit{C. Wang}, Bull. Aust. Math. Soc. 99, No. 3, 362--368 (2019; Zbl 1479.11009) Full Text: DOI
Straub, Armin Supercongruences for polynomial analogs of the Apéry numbers. (English) Zbl 1442.11039 Proc. Am. Math. Soc. 147, No. 3, 1023-1036 (2019). Reviewer: Thomas Ernst (Uppsala) MSC: 11B65 05A30 11B83 PDFBibTeX XMLCite \textit{A. Straub}, Proc. Am. Math. Soc. 147, No. 3, 1023--1036 (2019; Zbl 1442.11039) Full Text: DOI arXiv
Osburn, Robert; Straub, Armin; Zudilin, Wadim A modular supercongruence for \({}_6 F_5\): an Apéry-like story. (Une supercongruence modulaire pour \({}_6 F_5\): un conte à la Apéry.) (English. French summary) Zbl 1429.11039 Ann. Inst. Fourier 68, No. 5, 1987-2004 (2018). MSC: 11B65 33C20 33F10 11F30 PDFBibTeX XMLCite \textit{R. Osburn} et al., Ann. Inst. Fourier 68, No. 5, 1987--2004 (2018; Zbl 1429.11039) Full Text: DOI arXiv
Delaygue, É. Arithmetic properties of Apéry-like numbers. (English) Zbl 1441.11033 Compos. Math. 154, No. 2, 249-274 (2018). Reviewer: Luis Gallardo (Brest) MSC: 11B50 11B65 05A10 PDFBibTeX XMLCite \textit{É. Delaygue}, Compos. Math. 154, No. 2, 249--274 (2018; Zbl 1441.11033) Full Text: DOI arXiv
Cooper, Shaun; Wan, James G.; Zudilin, Wadim Holonomic alchemy and series for \(1/\pi \). (English) Zbl 1391.11165 Andrews, George E. (ed.) et al., Analytic number theory, modular forms and \(q\)-hypergeometric series. In honor of Krishna Alladi’s 60th birthday, University of Florida, Gainesville, FL, USA, March 17–21, 2016. Cham: Springer (ISBN 978-3-319-68375-1/hbk; 978-3-319-68376-8/ebook). Springer Proceedings in Mathematics & Statistics 221, 179-205 (2017). MSC: 11Y60 11F11 11B65 PDFBibTeX XMLCite \textit{S. Cooper} et al., Springer Proc. Math. Stat. 221, 179--205 (2017; Zbl 1391.11165) Full Text: DOI arXiv
Kimoto, Kazufumi Generalized Apéry-like numbers arising from the non-commutative harmonic oscillator. (English) Zbl 1361.11054 Ryukyu Math. J. 29, 1-31 (2016). MSC: 11M41 11B65 33E20 PDFBibTeX XMLCite \textit{K. Kimoto}, Ryukyu Math. J. 29, 1--31 (2016; Zbl 1361.11054)
Sun, Zhi-Wei Congruences involving \(g_n(x)=\sum\limits_{k=0}^n\dbinom{n}{k}^2\dbinom{2k}{k}x^k\). (English) Zbl 1366.11006 Ramanujan J. 40, No. 3, 511-533 (2016). MSC: 11A07 11B65 05A10 PDFBibTeX XMLCite \textit{Z.-W. Sun}, Ramanujan J. 40, No. 3, 511--533 (2016; Zbl 1366.11006) Full Text: DOI
Long, Ling; Osburn, Robert; Swisher, Holly On a conjecture of Kimoto and Wakayama. (English) Zbl 1402.11111 Proc. Am. Math. Soc. 144, No. 10, 4319-4327 (2016). MSC: 11M36 33C20 11B65 PDFBibTeX XMLCite \textit{L. Long} et al., Proc. Am. Math. Soc. 144, No. 10, 4319--4327 (2016; Zbl 1402.11111) Full Text: DOI arXiv
Mingarelli, Angelo B. Some conjectures in elementary number theory. (English) Zbl 1385.11047 Int. J. Math. Comput. Sci. 9, No. 2, 99-105 (2014). MSC: 11J72 11B65 05A10 PDFBibTeX XMLCite \textit{A. B. Mingarelli}, Int. J. Math. Comput. Sci. 9, No. 2, 99--105 (2014; Zbl 1385.11047) Full Text: arXiv
Yang, Peng; Cai, Tianxin On the divisibility of multinomial exponent sums. (English) Zbl 1313.11003 Adv. Math., Beijing 43, No. 3, 387-397 (2014). MSC: 11A05 11B39 11B65 PDFBibTeX XMLCite \textit{P. Yang} and \textit{T. Cai}, Adv. Math., Beijing 43, No. 3, 387--397 (2014; Zbl 1313.11003)
Kazalicki, Matija Modular forms, hypergeometric functions and congruences. (English) Zbl 1312.11017 Ramanujan J. 34, No. 1, 1-9 (2014). MSC: 11B83 11B65 11A07 11F30 11F37 PDFBibTeX XMLCite \textit{M. Kazalicki}, Ramanujan J. 34, No. 1, 1--9 (2014; Zbl 1312.11017) Full Text: DOI arXiv
Sun, Zhi-Wei Congruences for Franel numbers. (English) Zbl 1281.05007 Adv. Appl. Math. 51, No. 4, 524-535 (2013). MSC: 05A10 11A07 11B65 PDFBibTeX XMLCite \textit{Z.-W. Sun}, Adv. Appl. Math. 51, No. 4, 524--535 (2013; Zbl 1281.05007) Full Text: DOI arXiv
Luca, Florian; Stănică, Pantelimon On some conjectures on the monotonicity of some arithmetical sequences. (English) Zbl 1339.11038 J. Comb. Number Theory 4, No. 2, 115-123 (2012). Reviewer: Stephan Wagner (Stellenbosch) MSC: 11B83 11B65 11B68 05A10 PDFBibTeX XMLCite \textit{F. Luca} and \textit{P. Stănică}, J. Comb. Number Theory 4, No. 2, 115--123 (2012; Zbl 1339.11038)
Hessami Pilehrood, Kh.; Hessami Pilehrood, T. Congruences arising from Apéry-type series for zeta values. (English) Zbl 1293.11030 Adv. Appl. Math. 49, No. 3-5, 218-238 (2012). Reviewer: Romeo Meštrović (Kotor) MSC: 11B65 05A10 11B68 11A07 33F10 11B39 11M06 PDFBibTeX XMLCite \textit{Kh. Hessami Pilehrood} and \textit{T. Hessami Pilehrood}, Adv. Appl. Math. 49, No. 3--5, 218--238 (2012; Zbl 1293.11030) Full Text: DOI arXiv
Guo, Victor J. W.; Zeng, Jiang New congruences for sums involving Apéry numbers or central Delannoy numbers. (English) Zbl 1268.11028 Int. J. Number Theory 8, No. 8, 2003-2016 (2012). Reviewer: Enzo Bonacci (Latina) MSC: 11B65 05A10 11A07 PDFBibTeX XMLCite \textit{V. J. W. Guo} and \textit{J. Zeng}, Int. J. Number Theory 8, No. 8, 2003--2016 (2012; Zbl 1268.11028) Full Text: DOI arXiv
Sun, Zhi-Wei On sums of Apéry polynomials and related congruences. (English) Zbl 1275.11038 J. Number Theory 132, No. 11, 2673-2699 (2012). MSC: 11B65 05A10 11A07 11B68 PDFBibTeX XMLCite \textit{Z.-W. Sun}, J. Number Theory 132, No. 11, 2673--2699 (2012; Zbl 1275.11038) Full Text: DOI arXiv
Chan, Heng Huat; Kontogeorgis, Aristides; Krattenthaler, Christian; Osburn, Robert Supercongruences satisfied by coefficients of \(_2F_1\) hypergeometric series. (English. French summary) Zbl 1236.33006 Ann. Sci. Math. Qué. 34, No. 1, 25-36 (2010). Reviewer: Jürgen Wolfart (Frankfurt am Main) MSC: 33C05 05A10 11B65 11F11 PDFBibTeX XMLCite \textit{H. H. Chan} et al., Ann. Sci. Math. Qué. 34, No. 1, 25--36 (2010; Zbl 1236.33006) Full Text: arXiv
Chan, Heng Huat; Zudilin, Wadim New representations for Apéry-like sequences. (English) Zbl 1275.11035 Mathematika 56, No. 1, 107-117 (2010). Reviewer: Enzo Bonacci (Latina) MSC: 11B65 11F11 11F20 33C20 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{W. Zudilin}, Mathematika 56, No. 1, 107--117 (2010; Zbl 1275.11035) Full Text: DOI
Chu, Wenchang; Zheng, Deyin Infinite series with harmonic numbers and central binomial coefficients. (English) Zbl 1191.05014 Int. J. Number Theory 5, No. 3, 429-448 (2009). MSC: 05A19 11B65 33C05 PDFBibTeX XMLCite \textit{W. Chu} and \textit{D. Zheng}, Int. J. Number Theory 5, No. 3, 429--448 (2009; Zbl 1191.05014) Full Text: DOI
Luca, Florian; Shparlinski, Igor E. Arithmetic properties of Apéry numbers. (English) Zbl 1222.11040 J. Lond. Math. Soc., II. Ser. 78, No. 3, 545-562 (2008). Reviewer: Herman J. Tiersma (Den Haag) MSC: 11B83 11B37 11B65 11D45 PDFBibTeX XMLCite \textit{F. Luca} and \textit{I. E. Shparlinski}, J. Lond. Math. Soc., II. Ser. 78, No. 3, 545--562 (2008; Zbl 1222.11040) Full Text: DOI
Garaev, Moubariz Z.; Luca, Florian; Shparlinski, Igor E. Catalan and Apéry numbers in residue classes. (English) Zbl 1101.11010 J. Comb. Theory, Ser. A 113, No. 5, 851-865 (2006). Reviewer: Tom M. Apostol (Pasadena) MSC: 11B65 11A07 11B75 05A10 PDFBibTeX XMLCite \textit{M. Z. Garaev} et al., J. Comb. Theory, Ser. A 113, No. 5, 851--865 (2006; Zbl 1101.11010) Full Text: DOI
Zudilin, W. On the inverse Legendre transform of a certain family of sequences. (English. Russian original) Zbl 1216.11027 Math. Notes 76, No. 2, 276-279 (2004); translation from Mat. Zametki 76, No. 2, 300-303 (2004). Reviewer: Olaf Ninnemann (Berlin) MSC: 11B65 33C45 PDFBibTeX XMLCite \textit{W. Zudilin}, Math. Notes 76, No. 2, 276--279 (2004; Zbl 1216.11027); translation from Mat. Zametki 76, No. 2, 300--303 (2004) Full Text: DOI
Allouche, Jean-Paul A remark on Apéry’s numbers. (English) Zbl 0911.11003 J. Comput. Appl. Math. 83, No. 1, 123-125 (1997). MSC: 11A07 11B65 05A10 PDFBibTeX XMLCite \textit{J.-P. Allouche}, J. Comput. Appl. Math. 83, No. 1, 123--125 (1997; Zbl 0911.11003) Full Text: DOI
Yeung, Kit Ming On congruence for Apéry numbers. (English) Zbl 0844.11018 Southeast Asian Bull. Math. 20, No. 1, 103-110 (1996). Reviewer: József Sándor (Jud.Harghita) MSC: 11B65 11B75 PDFBibTeX XMLCite \textit{K. M. Yeung}, Southeast Asian Bull. Math. 20, No. 1, 103--110 (1996; Zbl 0844.11018)
Radoux, Christian Some arithmetical properties of Apéry numbers. (English) Zbl 0859.11004 J. Comput. Appl. Math. 64, No. 1-2, 11-19 (1995). Reviewer: József Sándor (Jud.Harghita) MSC: 11A07 11B83 11B65 PDFBibTeX XMLCite \textit{C. Radoux}, J. Comput. Appl. Math. 64, No. 1--2, 11--19 (1995; Zbl 0859.11004) Full Text: DOI
Strehl, Volker Recurrences and Legendre transform. (English) Zbl 0903.11008 Sémin. Lothar. Comb. 29, B29b, 22 p. (1992). MSC: 11B83 11B37 05A19 11B65 PDFBibTeX XMLCite \textit{V. Strehl}, Sémin. Lothar. Comb. 29, B29b, 22 p. (1992; Zbl 0903.11008) Full Text: EuDML
Coster, Matthijs J. Supercongruences. (English) Zbl 0715.11071 P-adic analysis, Proc. Int. Conf., Trento/Italy 1989, Lect. Notes Math. 1454, 194-204 (1990). Reviewer: L. van Hamme MSC: 11S31 11B65 PDFBibTeX XML
Van Hamme, L. Proof of a conjecture of Beukers on Apéry numbers. (English) Zbl 0634.10004 p-adic analysis, Proc. Conf., Houthalen/Belg. 1986, 189-195 (1986). Reviewer: Frits Beukers (Utrecht) MSC: 11A07 11B65 PDFBibTeX XML