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

Location: A3.339
Organizer: Prof. Dr. Jürgen Klüners

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

Abstract:

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.