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Bounds for theta sums in higher rank II

Number Theory 2023-05-12 v1

Abstract

In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.

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Cite

@article{arxiv.2305.06995,
  title  = {Bounds for theta sums in higher rank II},
  author = {Jens Marklof and Matthew Welsh},
  journal= {arXiv preprint arXiv:2305.06995},
  year   = {2023}
}

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26 pages