Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 117-137
Citer cet article
E. P. Golubeva; O. M. Fomenko. Значения рядов Дирихле, ассоциированных с модулярными формами, в точках $s=\frac12,1$. Zapiski Nauchnykh Seminarov POMI, Automorphic functions and number theory. Part II, Tome 134 (1984), pp. 117-137. http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a5/
@article{ZNSL_1984_134_a5,
author = {E. P. Golubeva and O. M. Fomenko},
title = {{\CYRZ}{\cyrn}{\cyra}{\cyrch}{\cyre}{\cyrn}{\cyri}{\cyrya} {\cyrr}{\cyrya}{\cyrd}{\cyro}{\cyrv} {{\CYRD}{\cyri}{\cyrr}{\cyri}{\cyrh}{\cyrl}{\cyre},} {\cyra}{\cyrs}{\cyrs}{\cyro}{\cyrc}{\cyri}{\cyri}{\cyrr}{\cyro}{\cyrv}{\cyra}{\cyrn}{\cyrn}{\cyrery}{\cyrh} {\cyrs}~{\cyrm}{\cyro}{\cyrd}{\cyru}{\cyrl}{\cyrya}{\cyrr}{\cyrn}{\cyrery}{\cyrm}{\cyri} {\cyrf}{\cyro}{\cyrr}{\cyrm}{\cyra}{\cyrm}{\cyri}, {\cyrv}~{\cyrt}{\cyro}{\cyrch}{\cyrk}{\cyra}{\cyrh} $s=\frac12,1$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {117--137},
year = {1984},
volume = {134},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a5/}
}
TY - JOUR
AU - E. P. Golubeva
AU - O. M. Fomenko
TI - Значения рядов Дирихле, ассоциированных с модулярными формами, в точках $s=\frac12,1$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1984
SP - 117
EP - 137
VL - 134
UR - http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a5/
LA - ru
ID - ZNSL_1984_134_a5
ER -
%0 Journal Article
%A E. P. Golubeva
%A O. M. Fomenko
%T Значения рядов Дирихле, ассоциированных с модулярными формами, в точках $s=\frac12,1$
%J Zapiski Nauchnykh Seminarov POMI
%D 1984
%P 117-137
%V 134
%U http://geodesic.mathdoc.fr/item/ZNSL_1984_134_a5/
%G ru
%F ZNSL_1984_134_a5
Let $f(z)=\sum_{n=1}^\infty a(n)e^{2\pi inz}$ be a cusp form of even weight $k$ which is an eigenfunction of all Hecke operators, $\chi$ a real character $\mod d$, $L_f(s,\chi)=\sum_{n=1}^\infty\chi(n)a(n)n^{-s-\frac{k-1}2}$. It is known that $L_f(s,\chi)$ satisfies a functional equation of Riemann type under $s\to1-s$. The authors prove some asymptotic results on $L_f(\frac12, \chi)$, $L_f(1, \chi)$, $d\to\infty$.
