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Higher depth mock theta functions and q-hypergeometric series

Authors
  • Males, Joshua1
  • Mono, Andreas1
  • Rolen, Larry2
  • 1 University of Cologne, Division of Mathematics, Weyertal 86-90, 50931 , (Germany)
  • 2 Vanderbilt University, 1420 Stevenson Center, TN 37240 , (United States)
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
May 19, 2021
Volume
33
Issue
4
Pages
857–866
Identifiers
DOI: 10.1515/forum-2021-0013
Source
De Gruyter
Keywords
License
Yellow

Abstract

In the theory of harmonic Maaß forms and mock modular forms, mock theta functions are distinguished examples which arose from q-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms, which we call higher depth mock theta functions, and develop q-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a q-hypergeometric series.

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