- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Twisted quadratic moments for Dirichlet $L$-functions Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 2095-2105 https://doi.org/10.4134/BKMS.2015.52.6.2095Published online November 30, 2015 St\'ephane R. Louboutin 163 Avenue de Luminy, Case 907 Abstract : Given $c$, a positive integer, we set $$M(f,c) :={2\over\phi (f)}\sum_{\chi\in X_f^-}\chi (c)\vert L(1,\chi)\vert^2,$$ where $X_f^-$ is the set of the $\phi (f)/2$ odd Dirichlet characters mod $f>2$, with $\gcd (f,c)=1$. We point out several mistakes in recently published papers and we give explicit closed formulas for the $f$'s such that their prime divisors are all equal to $\pm 1$ modulo $c$. As a Corollary, we obtain closed formulas for $M(f,c)$ for $c\in\{1,2,3,4,5, 6,8,10\}$. We also discuss the case of twisted quadratic moments for primitive characters. Keywords : $L$-function, character, mean values, moments MSC numbers : Primary 11M20 Downloads: Full-text PDF