Eric Mortenson - A heuristic guide to evaluating triple-sums

hrj:7431 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - https://doi.org/10.46298/hrj.2021.7431
A heuristic guide to evaluating triple-sums

Authors: Eric Mortenson

Using a heuristic that relates Appell-Lerch functions to divergent partial theta functions one can expand Hecke-type double-sums in terms of Appell-Lerch functions. We give examples where the heuristic can be used as a guide to evaluate analogous triple-sums in terms of Appell-Lerch functions or false theta functions.

https://doi.org/10.46298/hrj.2021.7431
Source : oai:HAL:hal-03208492v1
Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan
Published on: May 6, 2021
Submitted on: April 30, 2021
Keywords: false theta functions,mock theta functions,Appell-Lerch functions,Hecke-type triple-sums,2010 Mathematics Subject Classification. 11B65, 11F27,[MATH]Mathematics [math]


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