Exponential sums with sparse polynomials over finite fields

Igor E. Shparlinski; Qiang Wang

Exponential sums with sparse polynomials over finite fields

Number Theory 2020-07-30 v1

Authors: Igor E. Shparlinski , Qiang Wang

Abstract

We obtain new bounds of exponential sums modulo a prime $p$ with sparse polynomials $a_0x^{n_0} + \cdots + a_{\nu}x^{n_\nu}$ . The bounds depend on various greatest common divisors of exponents $n_0, \ldots, n_\nu$ and their differences. In particular, two new bounds for binomials are obtained, improving previous results in broad ranges of parameters.

Keywords

exponential sums upper bounds polynomials over finite fields

Cite

@article{arxiv.2007.14551,
  title  = {Exponential sums with sparse polynomials over finite fields},
  author = {Igor E. Shparlinski and Qiang Wang},
  journal= {arXiv preprint arXiv:2007.14551},
  year   = {2020}
}

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