Séminaire de Théorie des Nombres de Montpellier
lundi 07 mars 2005 à -
Valentin Blomer (Georg-August-Universität Göttingen)
« Estimates on representation numbers of quadratic forms »
Let $f$ be a primitive positive binary quadratic form having discriminant $-D$, and let $r_f(n)$ be the number of representations of $f$ by $n$. We give estimates and asymptotics for the moments $\sum_{n \leq x} r_f(n)^{\beta}$ for arbitrary $\beta \geq 0$, uniformly in $D = o(x)$. This is joint with A. Granville.