• On Partial Sums of a Spectral Analogue of the Möbius Function

• Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/123/02/0193-0201

• Keywords

Riemann zeta function; Maaß forms; 𝐿-functions.

• Abstract

Sankaranarayanan and Sengupta introduced the function $\mu^∗(n)$ corresponding to the Möbius function. This is defined by the coefficients of the Dirichlet series $1/L_f(s)$, where $L_f(s)$ denotes the 𝐿-function attached to an even Maaß cusp form 𝑓. We will examine partial sums of $\mu^∗(n)$. The main result is $\Sigma_{n\leq x}\mu^∗(n)=O(x \exp(-A\sqrt{\log x}))$, where 𝐴 is a positive constant. It seems to be the corresponding prime number theorem.

• Author Affiliations

2. Faculty of Science, Kyoto Sangyo University, Kamigamo, Kita-ku, Kyoto 603-8555, Japan

• Proceedings – Mathematical Sciences

Volume 131, 2021
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Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019