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Mean square of zeta function, circle problem and divisor problem revisited

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arxiv 1709.04340 v2 pith:TPE65RFG submitted 2017-09-13 math.AP math.NT

Jean Bourgain , Nigel Watt This is my paper · ORCID
classification math.APmath.NT
keywords bw17problemrelatedauthorscirclecloselydivisorelaborate
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This paper is closely related to the recent work [BW17] of the same authors and our purpose is to elaborate more on some of the results and methods from [BW17]. More specifically our goal is two-fold. Firstly, we will indicate how a simple variant related to Section 4 in [BW17] leads to the following improvements of Theorem 3 in [BW17]

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Bessel functions and Weyl's law for balls and spherical shells

    math.CA 2024-12 conditional novelty 6.0 of 10

    The authors improve Weyl remainder estimates for balls and spherical shells in all dimensions and prove new facts about zeros of Bessel cross-products.

  2. The Eighth Power Moments of $\Delta(x)$

    math.NT 2025-07 conditional novelty 3.0 of 10

    The paper claims an asymptotic formula for the integral of Delta(x)^8 from 2 to X, with error O(X^{3-1/254+epsilon}) and constants defined by two divisor-function sums.

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