A generalized supercongruence of Kimoto and Wakayama

DOI10.1016/j.jmaa.2018.05.031zbMath1406.11006OpenAlexW2804059232MaRDI QIDQ1659276

Ji-Cai Liu

Publication date: 15 August 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.05.031

zbMATH Keywords

Bernoulli numbersupercongruencespectral zeta functionApéry-like number

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Congruences; primitive roots; residue systems (11A07) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items

Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals, On two congruences involving Franel numbers, A supercongruence relation among Ap, Number Theoretic Study in Quantum Interactions, Congruences related to dual sequences and Catalan numbers, On two supercongruences involving Almkvist-Zudilin sequences, ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS, Heat kernel for the quantum Rabi model: II. Propagators and spectral determinants

Uses Software

• SIGMA
• MultiZeilberger

Cites Work

• Unnamed Item
• Proof of Sun's conjectures on integer-valued polynomials
• Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
• Some congruences for the Apéry numbers
• Supercongruences involving dual sequences
• Proof of some divisibility results on sums involving binomial coefficients
• Symbolic summation assists combinatorics
• Oscillator representations and systems of ordinary differential equations
• On a conjecture of Kimoto and Wakayama
• APÉRY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS
• CONGRUENCES SATISFIED BY APÉRY-LIKE NUMBERS