Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 155-165
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O. M. Fomenko. On the distribution of the roots of a quadratic congruence. Zapiski Nauchnykh Seminarov POMI, Modular functions and quadratic forms. Part 1, Tome 183 (1990), pp. 155-165. http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a7/
@article{ZNSL_1990_183_a7,
author = {O. M. Fomenko},
title = {On the distribution of the roots of a quadratic congruence},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {155--165},
year = {1990},
volume = {183},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a7/}
}
TY - JOUR
AU - O. M. Fomenko
TI - On the distribution of the roots of a quadratic congruence
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1990
SP - 155
EP - 165
VL - 183
UR - http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a7/
LA - ru
ID - ZNSL_1990_183_a7
ER -
%0 Journal Article
%A O. M. Fomenko
%T On the distribution of the roots of a quadratic congruence
%J Zapiski Nauchnykh Seminarov POMI
%D 1990
%P 155-165
%V 183
%U http://geodesic.mathdoc.fr/item/ZNSL_1990_183_a7/
%G ru
%F ZNSL_1990_183_a7
The author obtains the following estimate $$ \sum_{d\leqslant x}\,\sum_{\begin{subarray}{c}{0<f\leqslant d}\\{f^2+2rf-\beta\equiv0 \pmod{d}}\end{subarray}}\left(\frac fd\right)\ll x^{\frac58+\varepsilon}, $$ where $\left(\frac fd\right)$ is the Kronecker symbol and $\beta\ne\Box$, $r^2+\beta\ne\Box$.
