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