Sur la fonction Delta de Hooley associée à des caractères

Abstract

Let $(f_1,f_2)$ a $2$-tuple of arithmetic functions and $${\Delta }_3(n,f_1,f_2):=\underset{\begin{array}{c}(u_1,u_2)\in {\mathbb{R}}^2\\ (v_1,v_2)\in [0,1{]}^2\end{array}}{\sup }|\sum _{\begin{array}{c}{d}_1{d}_2\mid n\\ e^{u_i}<d_i⩽e^{u_i+v_i}\end{array}}{f}_1(d_1)f_2(d_2)|.$$ In this paper, we give an upper bound of the second moment of ${\Delta }_3(n,{\chi }_1,{\chi }_2)$ when ${\chi }_1$ and ${\chi }_2$ are two non principal Dirichlet characters, following methods developed by La Bretèche and Tenenbaum. This upper bound is a main step for the asymptotic counting of the number of ideals of norm fixed, which will be developped in another article.

In French

Cited by in corpus (1)

• Sur le nombre d'idéaux dont la norme est la valeur d'une forme binaire de degré 3