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Using Bailey’s $$_{10}\phi _9$$ 10 ϕ 9 transformation formula, we prove a family of q -congruences modulo the square of a cyclotomic polynomial, which were previously observed by the author… Click to show full abstract
Using Bailey’s $$_{10}\phi _9$$ 10 ϕ 9 transformation formula, we prove a family of q -congruences modulo the square of a cyclotomic polynomial, which were previously observed by the author and Zudilin (J Math Anal Appl 475:1636–1646, 2019). As an application, we confirm a conjecture in (Electron Res Arch 28:1031–1036, 2020). This also partially reproves a special case of Swisher’s (H.3) conjecture.
Keywords:
modulo square;
cyclotomic polynomial;
square cyclotomic;
family congruences;
congruences modulo
Journal Title: Results in Mathematics
Year Published: 2021
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Journal Title: Results in Mathematics
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!