Geometrija, obrazovanje i vizualizacija sa primenama, 7. novembar 2019.

Naredni sastanak Seminara biće održan u četvrtak, 7. novembra 2019. u sali 301f Matematičkog instituta SANU sa početkom u 17:15.

Predavač: Dragan Đokić, Matematički fakultet, Univerzitet u Beogradu

Naslov predavanja: LARGE VALUES AND THE FOURTH MOMENT OF DIRICHLET L-FUNCTIONS OVER FUNCTION FIELDS

Apstrakt: We will give a review about some properties of function fields and Dirichlet L-functions over function fields, and then present some new results. We establish the existence of large values of Dirichlet L-functions in the family of non-principal characters associated to prime polynomials Q over finite field F_q, as deg Q tends to infinity and s ∈ (1/2,1]. When s = 1, we provide a lower bound for the number of such characters. To do this, we adapt the Voronin resonance method to the function field setting. We also investigate this problem at the central point |L(1/2,χ)|, where now χ varies over even, non-principal, Dirichlet characters. In addition to resonance method, in this case we use an adaptation of Gal type sums estimate. N. Tamam considered the fourth moment of L-functions in central point 1/2, as deg Q tends to infinity, and established a partial main term, with only the leading order summand. In order to obtain the full main term, with all lower order summands, we consider the fourth moment additionally averaged over the critical circle The obtained asymptotic formula is in agreement with the existing conjectures for integral moments of L-functions in families.



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