Special hypergeometric motives and their $L$-functions: Asai recognition

Alexei Panchishkin; John Voight; Lassina Demb\'el\'e; Wadim Zudilin

Special hypergeometric motives and their $L$-functions: Asai recognition

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arxiv 1906.07384 v3 pith:QSI4GWDR submitted 2019-06-18 math.NT hep-thmath.AGmath.CAmath.CO

Lassina Dembélé , Alexei Panchishkin , John Voight , Wadim Zudilin This is my paper · ORCID

classification math.NThep-thmath.AGmath.CAmath.CO

keywords asaifunctionshypergeometricmotivesspecialarisingcenturycertain

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abstract

We recognize certain special hypergeometric motives, related to and inspired by the discoveries of Ramanujan more than a century ago, as arising from Asai $L$-functions of Hilbert modular forms.

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Bilateral Ramanujan-like series for $1/\pi^k$ and their congruences
math.NT 2019-08 conditional novelty 6.0 of 10

A new bilateral semi-terminating identity for Ramanujan-type 1/π^k series is proved, and a family of supercongruences is conjectured with proofs of several rank-3 and rank-5 cases.

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