Proceedings of the London Mathematical Society· 2014Q1
Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
- 160citations
- Q1SCImago
- 2014year
Short summary
A new formula expresses Hecke-type double sums using Appell-Lerch sums, providing straightforward proofs for classical mock theta identities and a new proof of the mock theta conjectures.
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Key points
- Introduced a dual notion between partial theta functions and Appell–Lerch sums.
- Derived a formula expressing Hecke-type double sums in terms of Appell–Lerch sums.
- The formula proves classical Hecke-type sum identities and mock theta identities.
- Provided a new proof for the mock theta conjectures.
- Extended the application to positive-level string functions of affine Lie Algebra A 1 ( 1 ).
AI-generated from the title and abstract; the full text is not read.
Abstract
By introducing a dual notion between partial theta functions and Appell–Lerch sums, we find and prove a formula which expresses Hecke-type double sums in terms of Appell–Lerch sums. Not only does our formula prove classical Hecke-type sum identities such as those in work of Kac and Peterson on affine Lie Algebras and Hecke modular forms, but once we have the Hecke-type forms for Ramanujan's mock theta functions our formula gives straightforward proofs of many of the classical mock theta identities. Indeed, we obtain a new proof of the mock theta conjectures. Our formula also applies to positive-level string functions associated with admissible representations of the affine Lie Algebra A 1 ( 1 ) of Kac and Wakimoto.
The authors' abstract, as published at the source. Proceedings of the London Mathematical Society, 2014 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics