Mathematics Wiskunde

Friday 27 September 2019

Explicit bound on Siegel zeros of imaginary quadratic fields

Speaker: Mr Faratiana Brice Razakarinoro
Time: 14:00
Venue: Mathematics, Room 3001

We consider the Dirichlet L-functions associated with characters defined by the Kronecker’s symbol. It is known that these L-functions might have zeros very close to 1. These hypothetical zeros are called Siegel zeros. In 1975, Goldfeld and Schinzel proved an effective lower bound for distance of the Siegel zeros from 1. In the thesis, we made Goldfeld-Schinzel’s bound explicit for the case of primitive odd characters. In this presentation, I will first talk about imaginary quadratic fields, which are naturally related to primitive odd characters, then I will mention the steps in the proof of the result. I will also talk about a potential application of the explicit bound concerning the size of the torsion subgroup of a CM elliptic curve.