Congruences involving \binom2kk²\binom4k2km^-k

2011/04/15 by Zhi-Hong Sun, Sun, Zhi-Hong
Mathematics · #05A10 #05A19 #11E25 #11G07 #11L10 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 11A07 #Secondary 33C45 #math.CO #math.NT #msc:05A10 #msc:05A19 #msc:11A07 #msc:11E25 #msc:11G07 #msc:11L10 #msc:33C45

paper · pdf · doi:10.48550/arxiv.1104.3047

14 pages

openalex publication_date 2011/04/15 · arxiv created 2011/04/18 · arxiv updated 2011/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p>3 be a prime, and let m be an integer with p\nmid m. In the paper, by using the work of Ishii and Deuring's theorem for elliptic curves with complex multiplication we solve some conjectures of Zhi-Wei Sun concerning ∑_k=0^p-1\binom2kk²\binom4k2km^-k\mod p².

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