Ramanujan's $_{1}ψ_1$ summation, Hecke-type double sums, and Appell-Lerch sums

Eric Mortenson

doi:10.1007/s11139-012-9379-5

paper

Ramanujan's $_{1} ψ_{1}$ summation, Hecke-type double sums, and Appell-Lerch sums

arXiv:1208.1359 · doi:10.1007/s11139-012-9379-5

Abstract

We use a specialization of Ramanujan's $_{1} ψ_{1}$ summation to give a new proof of a recent formula of Hickerson and Mortenson which expands a special family of Hecke-type double sums in terms of Appell-Lerch sums and theta functions.

arXiv commentIdentity $(2.2)$ was known to L. Kronecker

Ramanujan's 1​ψ1​ summation, Hecke-type double sums, and Appell-Lerch sums

Abstract

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Ramanujan's $_{1} ψ_{1}$ summation, Hecke-type double sums, and Appell-Lerch sums