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
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@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},
publisher = {mathdoc},
volume = {64},
year = {1976},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_1976_64_a6/ %G ru %F ZNSL_1976_64_a6
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/