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Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

  • Simon Macourt,
    Department of Pure Mathematics, University of New South Wales, Sydney, Australia
  • Ilya D. Shkredov,
    Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, Russia
  • Igor E. Shparlinski,
    Department of Pure Mathematics, University of New South Wales, Sydney, Australia
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Abstract

We give a new bound on collinear triples in subgroups of prime finite fields and use it to give some new bounds on exponential sums with trinomials.
Keywords: exponential sum, sparse polynomial, trinomial exponential sum, sparse polynomial, trinomial
MSC Classifications: 11L07, 11T23 show english descriptions Estimates on exponential sums
Exponential sums
11L07 - Estimates on exponential sums
11T23 - Exponential sums
 

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