Explicit formulae for the mean value of products of values of Dirichlet L-functions at positive integers.
| Autor: | Louboutin, Stéphane R. |
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| Zdroj: | Proceedings of the American Mathematical Society; Nov2024, Vol. 152 Issue 11, p4623-4631, 9p |
| Abstrakt: | Let m\ge 1 be a rational integer. We give an explicit formula for the mean value \begin{equation*} \frac {2}{\phi (f)}\sum _{\chi (-1)=(-1)^m}\vert L(m,\chi)\vert ^2, \end{equation*} where \chi ranges over the \phi (f)/2 Dirichlet characters modulo f>2 with the same parity as m. We then adapt our proof to obtain explicit means values for products of the form L(m_1,\chi _1)\cdots L(m_{n-1},\chi _{n-1})\overline {L(m_n,\chi _1\cdots \chi _{n-1})}. [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
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