Zobrazeno 1 - 10
of 157
pro vyhledávání: '"Louboutin, Stéphane"'
Autor:
Louboutin, Stéphane R.
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 9, Pp 1201-1205 (2021)
The evenness and the values modulo $4$ of the lengths of the periods of the continued fraction expansions of $\sqrt{p}$ and $\sqrt{2p}$ for $p\equiv 3\pmod {4}$ a prime are known. Here we prove similar results for the continued fraction expansion of
Externí odkaz:
https://doaj.org/article/cbb6dc53562e4d05813bd8ec40ab4712
Autor:
Louboutin, Stéphane
An explicit formula for the quadratic mean value at $s=1$ of the Dirichlet $L$-functions associated with the odd Dirichlet characters modulo $f>2$ is known. Here we present a situation where we could prove an explicit formula for the quadratic mean v
Externí odkaz:
http://arxiv.org/abs/2406.02802
Autor:
Louboutin, Stéphane
Let $m\ge 1$ be a rational integer. We give an explicit formula for the mean value $$\frac{2}{\phi(f)}\sum_{\chi (-1)=(-1)^m}\vert L(m,\chi )\vert^2,$$ where $\chi$ ranges over the $\phi (f)/2$ Dirichlet characters modulo $f>2$ with the same parity a
Externí odkaz:
http://arxiv.org/abs/2405.17981
Autor:
Louboutin, Stéphane
As a consequence of their work, Bruce C. Berndt and Ronald J. Evans in 1977 and Larry Joel Goldstein and Michael Razar in 1976 obtained a formula for the square of the class number of an imaginary quadratic number field in terms of Dedekind sums. Her
Externí odkaz:
http://arxiv.org/abs/2303.14000
Autor:
Louboutin, Stéphane R., Munsch, Marc
An explicit formula for the mean value of $\vert L(1,\chi)\vert^2$ is known, where $\chi$ runs over all odd primitive Dirichlet characters of prime conductors $p$. Bounds on the relative class number of the cyclotomic field ${\mathbb Q}(\zeta_p)$ fol
Externí odkaz:
http://arxiv.org/abs/2205.01024
Autor:
Louboutin, Stéphane, Munsch, Marc
We prove an asymptotic formula for the mean-square average of $L$- functions associated to subgroups of characters of sufficiently large size. Our proof relies on the study of certain character sums ${\cal A}(p,d)$ recently introduced by E. Elma. We
Externí odkaz:
http://arxiv.org/abs/2007.02623
Autor:
Louboutin, Stéphane R.
Publikováno v:
Proceedings of the American Mathematical Society; Nov2024, Vol. 152 Issue 11, p4623-4631, 9p
Autor:
Louboutin, Stéphane
Publikováno v:
Transactions of the American Mathematical Society, 2003 Aug 01. 355(8), 3079-3098.
Externí odkaz:
https://www.jstor.org/stable/1194919