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Четверг 10.09. Ю.В. Матиясевич: "Some numerical observations on number-theoretical properties of the theta functions of Dirichlet characters."

Четверг, 10 сентября, zoom. Начало в 14:00.

Докладчик: Ю.В. Матиясевич (ПОМИ).

Тема: Some numerical observations on number-theoretical properties of the theta functions of Dirichlet characters..

Abstract

We introduce two series of polynomials. Their definitions are motivated by
the functional equation of the theta function of Dirichlet character for some modulo q. We arrange these polynomials into non-degenerate square matrices. Certain
entries of the inverses of these matrices demonstrate surprising approximate periodicity with the length of the period equal to q. These periodicities were discovered
by computer calculations. The numerical data allow us to state a number of conjectures, but so far we found no theoretical explanation of these phenomena.
Preprint POMI 10/2026