Mathematical Notes· 2026Q2
A Further Common $$q$$-Extension of the (F.2) and (G.2) Supercongruences of Van Hamme
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- Q2SCImago
- 2026year
Short summary
A new $$q$$-supercongruence is proven modulo the cube of a cyclotomic polynomial, generalizing Van Hamme's (F.2) and (G.2) supercongruences.
AI-generated from the title and abstract; the full text is not read.
Key points
- A new $$q$$-supercongruence is proven modulo the cube of a cyclotomic polynomial.
- This congruence is a further common generalization of Van Hamme's (F.2) and (G.2) supercongruences.
- The proof employs Jackson's basic hypergeometric summation.
- The method of creative microscoping by Guo and Zudilin is a key ingredient in the proof.
AI-generated from the title and abstract; the full text is not read.
Abstract
In this paper, we prove a $$q$$ -supercongruence modulo the cube of a cyclotomic polynomial, which is a further common generalization of the (F.2) and (G.2) supercongruences of Van Hamme. The main ingredients of our proof include a basic hypergeometric summation by Jackson and the method of creative microscoping devised by Guo and Zudilin.
The authors' abstract, as published at the source. Mathematical Notes, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics