Estimates for representation numbers of quadratic forms
Blomer, Valentin ; Granville, Andrew
Duke Math. J., Tome 131 (2006) no. 1, p. 261-302 / Harvested from Project Euclid
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Let $f$ be a primitive positive integral binary quadratic form of discriminant $-D$ , and let $r_f(n)$ be the number of representations of $n$ by $f$ up to automorphisms of $f$ . In this article, we give estimates and asymptotics for the quantity $\sum_{n \leq x} r_f(n)^{\beta}$ for all $\beta \geq 0$ and uniformly in $D = o(x)$ . As a consequence, we get more-precise estimates for the number of integers which can be written as the sum of two powerful numbers
Publié le : 2006-11-01
Classification:  11E16,  11N56 
@article{1161093265,
     author = {Blomer, Valentin and Granville, Andrew},
     title = {Estimates for representation numbers of quadratic forms},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 261-302},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1161093265}
}

Blomer, Valentin; Granville, Andrew. Estimates for representation numbers of quadratic forms. Duke Math. J., Tome 131 (2006) no. 1, pp.  261-302. http://gdmltest.u-ga.fr/item/1161093265/