Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

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We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence of certain quantum modular forms related to Maass Eisenstein...

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Bibliographic Details
Main Authors: Zagier, Don (Author), Lewis, John B (Contributor)
Format: Article
Language:English
Published: Springer International Publishing, 2018-12-20T18:26:12Z.
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Online Access:Get fulltext
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100 1 0 |a Zagier, Don  |e author 
100 1 0 |a Lewis, John B  |e contributor 
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856 |z Get fulltext  |u http://hdl.handle.net/1721.1/119799 
520 |a We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence of certain quantum modular forms related to Maass Eisenstein series. 
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773 |t Research in the Mathematical Sciences 

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