• Kalyan Chakraborty

Articles written in Proceedings – Mathematical Sciences

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

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.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
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