Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 69-79
Citer cet article
E. P. Golubeva; O. M. Fomenko. Series $\sum F(m)q^m$, where $F(m)$ is the number of odd classes of binary quadratic forms of determinant $-m$. Zapiski Nauchnykh Seminarov POMI, Rings and modules, Tome 64 (1976), pp. 69-79. http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a6/
@article{ZNSL_1976_64_a6,
author = {E. P. Golubeva and O. M. Fomenko},
title = {Series $\sum F(m)q^m$, where $F(m)$ is the number of odd classes of binary quadratic forms of determinant~$-m$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {69--79},
year = {1976},
volume = {64},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a6/}
}
TY - JOUR
AU - E. P. Golubeva
AU - O. M. Fomenko
TI - Series $\sum F(m)q^m$, where $F(m)$ is the number of odd classes of binary quadratic forms of determinant $-m$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1976
SP - 69
EP - 79
VL - 64
UR - http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a6/
LA - ru
ID - ZNSL_1976_64_a6
ER -
%0 Journal Article
%A E. P. Golubeva
%A O. M. Fomenko
%T Series $\sum F(m)q^m$, where $F(m)$ is the number of odd classes of binary quadratic forms of determinant $-m$
%J Zapiski Nauchnykh Seminarov POMI
%D 1976
%P 69-79
%V 64
%U http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a6/
%G ru
%F ZNSL_1976_64_a6
Consideration of the analytic continuation of the Eisenstein series of weight $3/2$ for the group $\Gamma_0(4)$ leads to a new proof of Mordell's formula connecting the values $\chi(\omega)=\sum^\infty_{m=1}F(m)e^{\pi im\omega}$, $\operatorname{Im}\omega>0$, and $\chi(-\frac{1}{\omega})$. The behavior of the function $\chi(\omega)$for $\Gamma_0(4)$is examined by the same method.
