Keywords: supercongruence; Euler number; Almkvist-Zudilin sequence
@article{10_21136_CMJ_2021_0384_20,
author = {Liu, Ji-Cai and Ni, He-Xia},
title = {On two supercongruences involving {Almkvist-Zudilin} sequences},
journal = {Czechoslovak Mathematical Journal},
pages = {1211--1219},
year = {2021},
volume = {71},
number = {4},
doi = {10.21136/CMJ.2021.0384-20},
mrnumber = {4339123},
zbl = {07442486},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0384-20/}
}
TY - JOUR AU - Liu, Ji-Cai AU - Ni, He-Xia TI - On two supercongruences involving Almkvist-Zudilin sequences JO - Czechoslovak Mathematical Journal PY - 2021 SP - 1211 EP - 1219 VL - 71 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0384-20/ DO - 10.21136/CMJ.2021.0384-20 LA - en ID - 10_21136_CMJ_2021_0384_20 ER -
%0 Journal Article %A Liu, Ji-Cai %A Ni, He-Xia %T On two supercongruences involving Almkvist-Zudilin sequences %J Czechoslovak Mathematical Journal %D 2021 %P 1211-1219 %V 71 %N 4 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0384-20/ %R 10.21136/CMJ.2021.0384-20 %G en %F 10_21136_CMJ_2021_0384_20
Liu, Ji-Cai; Ni, He-Xia. On two supercongruences involving Almkvist-Zudilin sequences. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1211-1219. doi: 10.21136/CMJ.2021.0384-20
[1] Almkvist, G., Zudilin, W.: Differential equations, mirror maps and zeta values. Mirror Symmetry AMS/IP Studies in Advanced Mathematics 38. American Mathematical Society, Providence (2006), 481-515. | DOI | MR | JFM
[2] Amdeberhan, T., Tauraso, R.: Supercongruences for the Almkvist-Zudilin numbers. Acta Arith. 173 (2016), 255-268. | DOI | MR | JFM
[3] Apéry, R.: Irrationalité de $\zeta(2)$ et $\zeta(3)$. Astérisque 61 (1979), 11-13 French. | MR | JFM
[4] Beukers, F.: Some congruences for the Apéry numbers. J. Number Theory 21 (1985), 141-155. | DOI | MR | JFM
[5] Beukers, F.: Another congruence for the Apéry numbers. J. Number Theory 25 (1987), 201-210. | DOI | MR | JFM
[6] Chan, H. H., Cooper, S., Sica, F.: Congruences satisfied by Apéry-like numbers. Int. J. Number Theory 6 (2010), 89-97. | DOI | MR | JFM
[7] Coster, M. J.: Supercongruences: Ph.D. Thesis. Universiteit Leiden, Leiden (1988).
[8] Gessel, I.: Some congruences for Apéry numbers. J. Number Theory 14 (1982), 362-368. | DOI | MR | JFM
[9] Guo, V. J. W., Liu, J.-C.: Some congruences related to a congruence of Van Hamme. Integral Transforms Spec. Funct. 31 (2020), 221-231. | DOI | MR | JFM
[10] Guo, V. J. W., Zeng, J.: Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials. J. Number Theory 132 (2012), 1731-1740. | DOI | MR | JFM
[11] Lehmer, E.: On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson. Ann. Math. (2) 39 (1938), 350-360. | DOI | MR | JFM
[12] Liu, J.-C.: Proof of some divisibility results on sums involving binomial coefficients. J. Number Theory 180 (2017), 566-572. | DOI | MR | JFM
[13] Liu, J.-C.: A generalized supercongruence of Kimoto and Wakayama. J. Math. Anal. Appl. 467 (2018), 15-25. | DOI | MR | JFM
[14] Liu, J.-C.: On Van Hamme's (A.2) and (H.2) supercongruences. J. Math. Anal. Appl. 471 (2019), 613-622. | DOI | MR | JFM
[15] Liu, J.-C.: Semi-automated proof of supercongruences on partial sums of hypergeometric series. J. Symb. Comput. 93 (2019), 221-229. | DOI | MR | JFM
[16] Liu, J.-C.: On a sum of Apéry-like numbers arising from spectral zeta functions. Colloq. Math. 160 (2020), 1-6. | DOI | MR | JFM
[17] Liu, J.-C.: On two congruences involving Franel numbers. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 114 (2020), Article ID 201, 10 pages. | DOI | MR | JFM
[18] Liu, J.-C.: Some supercongruences arising from symbolic summation. J. Math. Anal. Appl. 488 (2020), Article ID 124062, 10 pages. | DOI | MR | JFM
[19] Liu, J.-C.: A supercongruence relation among Apéry-like numbers. Colloq. Math. 163 (2021), 333-340. | DOI | MR | JFM
[20] Liu, J.-C., Wang, C.: Congruences for the $(p-1)$th Apéry number. Bull. Aust. Math. Soc. 99 (2019), 362-368. | DOI | MR | JFM
[21] Mortenson, E.: Supercongruences between truncated $_2F_1$ hypergeometric functions and their Gaussian analogs. Trans. Am. Math. Soc. 355 (2003), 987-1007. | DOI | MR | JFM
[22] Osburn, R., Sahu, B.: Supercongruences for Apéry-like numbers. Adv. Appl. Math. 47 (2011), 631-638. | DOI | MR | JFM
[23] Osburn, R., Sahu, B., Straub, A.: Supercongruences for sporadic sequences. Proc. Edinb. Math. Soc., II. Ser. 59 (2016), 503-518. | DOI | MR | JFM
[24] Osburn, R., Schneider, C.: Gaussian hypergeometric series and supercongruences. Math. Comput. 78 (2009), 275-292. | DOI | MR | JFM
[25] Pan, H.: On divisibility of sums of Apéry polynomials. J. Number Theory 143 (2014), 214-223. | DOI | MR | JFM
[26] Schneider, C.: Symbolic summation assists combinatorics. Sémin. Lothar. Comb. 56 (2007), B56b, 36 pages. | MR | JFM
[27] Sun, Z.-H.: New congruences involving Apéry-like numbers. Available at , 24 pages. | arXiv
[28] Sun, Z.-W.: Super congruences and Euler numbers. Sci. China, Math. 54 (2011), 2509-2535. | DOI | MR | JFM
[29] Sun, Z.-W.: On sums of Apéry polynomials and related congruences. J. Number Theory 132 (2012), 2673-2699. | DOI | MR | JFM
[30] Sun, Z.-W.: A new series for $\pi^3$ and related congruences. Int. J. Math. 26 (2015), Article ID 1550055, 23 pages. | DOI | MR | JFM
[31] Wang, C.: Symbolic summation methods and hypergeometric supercongruences. J. Math. Anal. Appl. 488 (2020), Article ID 124068, 11 pages. | DOI | MR | JFM
[32] Wolstenholme, J.: On certain properties of prime numbers. Quart. J. Pure Appl. Math. 5 (1862), 35-39.
[33] Zagier, D.: Integral solutions of Apéry-like recurrence equations. Groups and Symmetries: From Neolithic Scots to John McKay CRM Proceedings and Lecture Notes 47. American Mathematical Society, Providence (2009), 349-366. | DOI | MR | JFM
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