Some new q-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial

We give some new [Formula: see text]-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial, respectively. One of them is related to the following congruence due to Deines, Fuselier, Long, Swisher, and Tu: for primes [Formula: see text], [Formula: see text] where [Formula: see text] denotes the [Formula: see text]-adic Gamma function. Our proof relies on Watson’s [Formula: see text] transformation and the “creative microscoping” method introduced by the first author and Zudilin.

Authors

Institutions

Publication Details

Journal
International Journal of Number Theory
Published
2026-11-06
DOI
https://doi.org/10.1142/s1793042127500254
Primary Topic
Advanced Mathematical Identities
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
NOV
article

Some new q-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial

Victor J. W. Guo, Jian-Ning Wu
International Journal of Number Theory
Advanced Mathematical Identities
article

Some new q-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial

Victor J. W. Guo, Jian-Ning Wu
article en

Abstract

We give some new [Formula: see text]-supercongruences modulo the fourth and fifth powers of a cyclotomic polynomial, respectively. One of them is related to the following congruence due to Deines, Fuselier, Long, Swisher, and Tu: for primes [Formula: see text], [Formula: see text] where [Formula: see text] denotes the [Formula: see text]-adic Gamma function. Our proof relies on Watson’s [Formula: see text] transformation and the “creative microscoping” method introduced by the first author and Zudilin.

International Journal of Number Theory
Hangzhou Normal University (CN)
Openalex Percentile: Top 15%
Advanced Mathematical Identities
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Laika access coming soon