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Sign changes of Kloosterman sums and exceptional characters

Abstract:
We prove that the existence of exceptional real zeros of Dirichlet Lfunctions would lead to cancellations in the sum p≤x Kl(1, p) of Kloosterman sums over primes, and also to sign changes of Kl(1, n), where n runs over integers with exactly two prime factors. Our arguments involve a variant of Bombieri’s sieve, bounds for twisted sums of Kloosterman sums, and work of Fouvry and Michel on sums of |Kl(1, n)|.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1090/proc/14239

Authors


Drappeau, S More by this author
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Magdalen College
ORCID:
0000-0001-5782-7082
Publisher:
American Mathematical Society Publisher's website
Journal:
Proceedings of the American Mathematical Society Journal website
Volume:
147
Issue:
1
Pages:
61-75
Publication date:
2018-10-03
Acceptance date:
2018-03-25
DOI:
EISSN:
1088-6826
ISSN:
0002-9939
Pubs id:
pubs:831688
URN:
uri:39cf3796-3f38-4795-9784-f8747837f108
UUID:
uuid:39cf3796-3f38-4795-9784-f8747837f108
Local pid:
pubs:831688

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