A heuristic guide to evaluating triple-sums

Eric T Mortenson (1)

1 SPBU - Saint Petersburg State University

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.

Mots clés: Hecke-type triple-sums; Appell-Lerch functions; mock theta functions; false theta functions

Domaines: Mathématiques [math]

Eric T Mortenson. A heuristic guide to evaluating triple-sums. Hardy-Ramanujan Journal, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020, pp.99-121. ⟨10.46298/hrj.2021.7431⟩. ⟨hal-03208492⟩