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1 results

  • Bilinear Kloosterman sums in function fields and the distribution of irreducible polynomials

  • Part of
  • Christian Bagshaw
  • Journal:
    Canadian Journal of Mathematics , First View
    Published online by Cambridge University Press:
    20 December 2024, pp. 1-26
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  • Inspired by the work of Bourgain and Garaev (2013), we provide new bounds for certain weighted bilinear Kloosterman sums in polynomial rings over a finite field. As an application, we build upon and extend some results of Sawin and Shusterman (2022). These results include bounds for exponential sums weighted by the Möbius function and a level of distribution for irreducible polynomials beyond 1/2, with arbitrary composite modulus. Additionally, we can do better when averaging over the modulus, to give an analogue of the Bombieri-Vinogradov Theorem with a level of distribution even further beyond 1/2.