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Square-root cancellation for sums of factorization functions over squarefree progressions in $mathbb F_q[t]$

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 نشر من قبل Will Sawin
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English
 تأليف Will Sawin




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We prove estimates for the level of distribution of the Mobius function, von Mangoldt function, and divisor functions in squarefree progressions in the ring of polynomials over a finite field. Each level of distribution converges to $1$ as $q$ goes to $infty$, and the power savings converges to square-root cancellation as $q$ goes to $infty$. These results in fact apply to a more general class of functions, the factorization functions, that includes these three. The divisor estimates have applications to the moments of $L$-functions, and the von Mangoldt estimate to one-level densities.



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