Alexander Mangerel: Short Sums of Dirichlet Characters

Tid: On 2018-11-14 kl 11.00 - 12.00

Föreläsare: Alexander Mangerel (Université de Montréal)

Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University

Abstract: In light of a classical conjecture of I.M. Vinogradov on quadratic non-residues modulo primes, it is of great interest to exhibit cancellation in partial sums of a given non-principal Dirichlet character modulo q on intervals \([1,q^{\epsilon}]\), for any \(\epsilon > 0\). Aside from an old result of Iwaniec (building on work of Postnikov) regarding short sums of characters to smooth moduli, there has been scant progress in proving such bounds even for specific subcollections of characters. 

In this talk, we construct a family of non-principal Dirichlet characters $\chi$ for which it can be shown that \(\sum_{1 \leq n \leq t} \chi(n) = o(t)\) for any \(t >q^{\epsilon}\), motivating our construction by drawing a parallel between the problem of estimating short character sums with that of estimating maximal character sums.

Tillhör: Institutionen för matematik
Senast ändrad: 2018-11-09