On the distribution of cubic exponential sums
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Benoît Louvel
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.
Funding source: Universität Göttingen
Award Identifier / Grant number: Graduiertenkolleg Gruppen und Geometrie 535
Funding source: EPFL Lausanne
This article is based on Chapter 2 and Chapter 4 of the author's PhD thesis [`Twisted Kloosterman sums and cubic exponential sums', Ph.D. thesis, Universität Göttingen, Université de Montpellier 2, 2008]. I sincerely thank my supervisors, Professor Samuel James Patterson and Professor Philippe Michel, for introducing me to the theory of exponential sums and for their support and encouragement. I also thank Professor Valentin Blomer for his advice and comments on this paper. I want to thank the École Polytechnique Fédérale de Lausanne and the Université de Montpellier 2, where part of this work has been done, for excellent working conditions.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Loop homology of spheres and complex projective spaces
- Symmetries of the positive semidefinite cone
- On the distribution of cubic exponential sums
- The tempered spectrum of quasi-split classical groups III: The odd orthogonal groups
- Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and q-zeta functions
- Multiplicative properties of Quinn spectra
- On the crossing number of semiadequate links
- “Spectral implies Tiling” for three intervals revisited
- Mock modular grids and Hecke relations for mock modular forms
Articles in the same Issue
- Frontmatter
- Loop homology of spheres and complex projective spaces
- Symmetries of the positive semidefinite cone
- On the distribution of cubic exponential sums
- The tempered spectrum of quasi-split classical groups III: The odd orthogonal groups
- Hyperbolic-sine analogues of Eisenstein series, generalized Hurwitz numbers, and q-zeta functions
- Multiplicative properties of Quinn spectra
- On the crossing number of semiadequate links
- “Spectral implies Tiling” for three intervals revisited
- Mock modular grids and Hecke relations for mock modular forms
