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      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

       

      Kalyan Chakraborty1 Makoto Minamide2

      1. Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
      2. Faculty of Science, Kyoto Sangyo University, Kamigamo, Kita-ku, Kyoto 603-8555, Japan
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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