## Kernels of $L$-functions and shifted convolutions

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- by Nikolaos Diamantis
- Proc. Amer. Math. Soc.
**148**(2020), 5059-5070 - DOI: https://doi.org/10.1090/proc/15182
- Published electronically: September 17, 2020
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## 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.## References

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## Bibliographic 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**148**(2020), 5059-5070 - MSC (2010): Primary 11F67, 11F68
- DOI: https://doi.org/10.1090/proc/15182
- MathSciNet review: 4163822