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arXiv · 1107.0197

On the distribution of cubic exponential sums

Benoit Louvel
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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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Benoit Louvel. 2011-07-01. On the distribution of cubic exponential sums. https://arxiv.org/abs/1107.0197

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