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On the distribution of cubic exponential sums

On the distribution of cubic exponential sums 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

On the distribution of cubic exponential sums

Forum Mathematicum , Volume 26 (4) – Jul 1, 2014

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Publisher
de Gruyter
Copyright
Copyright © 2014 by the
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.2011.167
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Forum Mathematicumde Gruyter

Published: Jul 1, 2014

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