Two problems related to the non-vanishing of $L(1,\chi )$

Codecà, Paolo, Dvornicich, Roberto, and Zannier, Umberto. "Two problems related to the non-vanishing of $L (1, \chi )$." Journal de théorie des nombres de Bordeaux 10.1 (1998): 49-64. <http://eudml.org/doc/248160>.

@article{Codecà1998,
abstract = {We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or $((xy/q)), (0 \le x, y &lt; q)$, where $((u)) = u - [u] - 1/2$ denotes the “centered” fractional part of $x$. These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet $L$-functions at $s = 1$.},
author = {Codecà, Paolo, Dvornicich, Roberto, Zannier, Umberto},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {arithmetic functions; Dirichlet -functions; Fourier series; ranks of matrices},
language = {eng},
number = {1},
pages = {49-64},
publisher = {Université Bordeaux I},
title = {Two problems related to the non-vanishing of $L (1, \chi )$},
url = {http://eudml.org/doc/248160},
volume = {10},
year = {1998},
}

TY - JOUR
AU - Codecà, Paolo
AU - Dvornicich, Roberto
AU - Zannier, Umberto
TI - Two problems related to the non-vanishing of $L (1, \chi )$
JO - Journal de théorie des nombres de Bordeaux
PY - 1998
PB - Université Bordeaux I
VL - 10
IS - 1
SP - 49
EP - 64
AB - We study two rather different problems, one arising from Diophantine geometry and one arising from Fourier analysis, which lead to very similar questions, namely to the study of the ranks of matrices with entries either zero or $((xy/q)), (0 \le x, y &lt; q)$, where $((u)) = u - [u] - 1/2$ denotes the “centered” fractional part of $x$. These ranks, in turn, are closely connected with the non-vanishing of the Dirichlet $L$-functions at $s = 1$.
LA - eng
KW - arithmetic functions; Dirichlet -functions; Fourier series; ranks of matrices
UR - http://eudml.org/doc/248160
ER -