Ramanujan's ₁psi₁ summation, Hecke-type double sums, and Appell-Lerch sums
classification
🧮 math.NT
keywords
sumsappell-lerchdoublehecke-typeramanujansummationexpandsfamily
read the original abstract
We use a specialization of Ramanujan's ${}_1\psi_1$ 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.
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