Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial

被引：0
作者：
Victor J. W. Guo
Michael J. Schlosser
机构：
[1] Huaiyin Normal University,School of Mathematics and Statistics
[2] Universität Wien,Fakultät für Mathematik
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2023年 / 117卷
关键词：
Basic hypergeometric series; Supercongruences; -congruences; Cyclotomic polynomial; Gasper’s summation; Primary 33D15 Secondary 11A07;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper, the method of creative microscoping (a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.
引用
收藏
相关论文
共 32 条
  • [1] Guo VJ (2020)-Supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping Adv. Appl. Math. 120 Art. 102078-835
  • [2] Guo VJ (2022)A new extension of the (A.2) supercongruence of Van Hamme Results Math. 77 Art. 96-302
  • [3] Guo VJW(2020)A family of Isr. J. Math. 240 821-1138
  • [4] Schlosser MJ(2020)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial Results Math. 75 Art. 155-358
  • [5] Guo VJW (2021)A new family of Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 Art. 132-215
  • [6] Schlosser MJ(2022)-supercongruences modulo the fourth power of a cyclotomic polynomial Bull. Aust. Math. Soc. 105 296-2000
  • [7] Guo VJW (2020)Some Proc. R. Soc. Edinb. Sect. A 150 1127-418
  • [8] Schlosser MJ(2019)-supercongruences modulo the square and cube of a cyclotomic polynomial Adv. Math. 346 329-711
  • [9] Guo VJW(2020)A family of C. R. Math. Acad. Sci. Paris 358 211-372
  • [10] Schlosser MJ(2022)-supercongruences modulo the cube of a cyclotomic polynomial Ann. Mat. Pura Appl. (4) 201 1993-391
1234