Kernels of $L$-functions and shifted convolutions
Author:
Nikolaos Diamantis
Journal:
Proc. Amer. Math. Soc. 148 (2020), 5059-5070
MSC (2010):
Primary 11F67, 11F68
DOI:
https://doi.org/10.1090/proc/15182
Published electronically:
September 17, 2020
MathSciNet review:
4163822
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Abstract | References | Similar Articles | Additional Information
Abstract: We propose a characterisation of the field into which quotients of non-critical values of $L$-functions associated to a cusp form belong. The construction involves shifted convolution series of divisor sums and a certain double Eisenstein series that induces a kernel of $L$-functions.
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Additional Information
Nikolaos Diamantis
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
ORCID:
0000-0002-3670-278X
Email:
nikolaos.diamantis@nottingham.ac.uk
Received by editor(s):
September 2, 2019
Received by editor(s) in revised form:
February 9, 2020
Published electronically:
September 17, 2020
Communicated by:
Benjamin Brubaker
Article copyright:
© Copyright 2020
American Mathematical Society