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December 2020 A note on Titchmarsh divisor problem under the generalized Riemann hypothesis
Hengcai Tang
Rocky Mountain J. Math. 50(6): 2223-2233 (December 2020). DOI: 10.1216/rmj.2020.50.2223

Abstract

Let Λ(n) be the von Mangoldt function and τ(n) the divisor function. We focus on the summation

T ( x ) = 1 < n x Λ ( n ) τ ( n 1 ) .

Under the Riemann hypothesis related to Dirichlet L-functions, it is proved that

T ( x ) = x P 1 ( log x ) + O ( x 1 𝜃 )

holds for 𝜃<16×104. Here P1(t) is a polynomial of degree 1.

Citation

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Hengcai Tang. "A note on Titchmarsh divisor problem under the generalized Riemann hypothesis." Rocky Mountain J. Math. 50 (6) 2223 - 2233, December 2020. https://doi.org/10.1216/rmj.2020.50.2223

Information

Received: 24 October 2019; Revised: 2 June 2020; Accepted: 4 June 2020; Published: December 2020
First available in Project Euclid: 5 January 2021

Digital Object Identifier: 10.1216/rmj.2020.50.2223

Subjects:
Primary: 11F30, 11L20, 11M06

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 6 • December 2020
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