Proof of a q-supercongruence conjectured by Guo and Schlosser

2020/05/29 by Long Li, Li, Long, Su-Dan Wang +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2005.14466

openalex publication_date 2020/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we confirm the following conjecture of Guo and Schlosser: for any odd integer n>1 and M=(n+1)/2 or n-1, ∑k=0M[4k-1]q2[4k-1]2\frac(q-2;q4)k4(q4;q4)k4q4k≡ (2q+2q-1-1)[n]q24\pmod[n]q24Φn(q2), where [n]=[n]q=(1-qn)/(1-q),(a;q)0=1,(a;q)k=(1-a)(1-aq)⋯(1-aqk-1) for k≥ 1 and Φn(q) denotes the n-th cyclotomic polynomial.

Citations

• A q-microscope for supercongruences

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