Ober­se­mi­nar "Num­ber Theo­ry and Arith­me­ti­cal Sta­ti­stics": Fran­cis­co Araú­jo (Bonn), Esti­ma­tes for the num­ber of re­pre­sen­ta­ti­ons of bi­na­ry qua­dra­tic forms

Ort: A3.339
Veranstalter: Prof. Dr. Jürgen Klüners

Titel: Estimates for the number of representations of binary quadratic forms


Given a positive definite binary quadratic form g, we study the number of representations of an integer by g, denoted rn(g).

In particular, we generalize an estimate of Blomer and Granville for the quantity ∑ n≤xrg(n)β with β a positive integer, to the case where g has a non fundamental discriminant. To do this, we study the non-maximal orders of imaginary quadratic number fields, and associated L-series.