Abstract
Evaluating the mean square averages of the Dirichlet $L$-functions over Dirichlet characters $\chi$ of the same parity is an active problem in number theory. Here we explicitly evaluate $\sum_{\chi\text{ odd}}L(3,\chi)$ using certain trigonometric sums and Bernoulli polynomials and express the sum in terms of the Euler totient function $\phi$ and the Jordan totient function $J_s$.
Citation
Neha Elizabeth Thomas. Arya Chandran. K. Vishnu Namboothiri. "On the mean square average of Dirichlet $L$-function over characters of odd parityin a special case." Funct. Approx. Comment. Math. 68 (1) 41 - 57, March 2023. https://doi.org/10.7169/facm/2020
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