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On the distribution of cubic exponential sums

Authors
  • Louvel, Benoît
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Nov 27, 2011
Volume
26
Issue
4
Pages
987–1028
Identifiers
DOI: 10.1515/form.2011.167
Source
De Gruyter
Keywords
License
Yellow

Abstract

Using the theory of metaplectic forms, we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estimates on average over arithmetic progressions are obtained. In the second part of the paper, we prove that the sign of cubic exponential sums changes infinitely often, as the modulus runs over almost prime integers.

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