On two mean square averages of Dirichlet $L$-function

Neha Elizabeth Thomas; Arya Chandran; K Vishnu Namboothiri

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arXiv · 2102.08844

On two mean square averages of Dirichlet $L$-function

Neha Elizabeth Thomas·Arya Chandran·K Vishnu Namboothiri

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Abstract

Finding the mean square averages of the Dirichlet $L$-functions over Dirichlet characters $\chi$ of same parity is an active problem in number theory. Here we explicitly evaluate such averages of $L(3,\chi)$ and $L(4,\chi)$ using certain trigonometric sums and Bernoulli polynomials and express them in terms of the Euler totient function $\phi$ and the Jordan totient function $J_s$.

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Neha Elizabeth Thomas, Arya Chandran, K Vishnu Namboothiri. 2021-02-17. On two mean square averages of Dirichlet $L$-function. https://arxiv.org/abs/2102.08844

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