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arXiv · 2401.10399

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

Christian Bagshaw
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Abstract

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 M\"obius 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.

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Christian Bagshaw. 2024-01-18. Bilinear Kloosterman sums in function fields and the distribution of irreducible polynomials. https://doi.org/10.4153/s0008414x24000956

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