Hypergeometric formulas for lattice sums and Mahler measures

2008/06/22 by Mathew D. Rogers, Rogers, Mathew D. · 2 citations
Mathematics · #11M41 #33C05 #33C20 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M41 #msc:33C05 #msc:33C20

paper · pdf · doi:10.48550/arxiv.0806.3590

27 pages, typos fixed

openalex publication_date 2008/06/22 · arxiv created 2010/12/28 · arxiv updated 2010/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a variety of explicit formulas relating special values of generalized hypergeometric functions to lattice sums with four indices of summation. These results are related to Boyd's conjectured identities between Mahler measures and special values of L-series of elliptic curves.

Cited by

• Mahler measures at interior CM points: proofs of two conjectures of Samart
• Samart's conjecture n₄(81)=40M₇: the exact CM evaluation and the two obstructions. A status report

Related

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