MSc (Mathematics) thesis defence talks
3:30 pm, Seminar Hall
On the Non vanishing of Dirichlet L functions using twisted molifier
Arghya Datta
Chennai Mathematical Institute.
15-04-19

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Abstract

The zeros of L-functions on the critical line are as important in number theory as they are mysterious.This talk will be the continuation of the previous talk that I gave during the research seminar regarding study the classical nonvanishing problem of primitive Dirichlet L-functions. It is conjectured that $L(\dfrac {1}{2},\chi)\neq 0$ for every Dirichlet character (mod p). In this talk , I plan to outline a proof (due to a recent work jointly done by Rizwanur Khan and Hieu T. Ngo) for at least $\dfrac {3}{8}$ of the primitive Dirichlet characters $\chi$ of large prime modulus , the central value $L(\dfrac {1}{2},\chi)$ does not vanish.