Oberseminar ZAHLENTHEORIE (online)
Probabilistic study of the Hurwitz zeta-function with algebraic parameter
| Date: | 12/02/2022, 9:00 AM - 11:15 AM |
| Category: | Fakultät für Mathematik und Informatik, Veranstaltung |
| Speaker: | Dr. Masahiro Mine (Sophia University, Tokyo) |
Dr. Masahiro Mine (Sophia University, Tokyo)
Probabilistic study of the Hurwitz zeta-function with algebraic parameter
Abstract. Cassels proved in 1961 that the Hurwitz zeta-function has infinitely many zeros for Re(s)>1 if the parameter is algebraic and irrational. A key step in his proof is to show at least 51% of log(n+alpha) are linearly independent over rational numbers. In this talk, I will introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. Then I explain how Cassels' method is applied in the study of the Hurwitz zeta-function with this random variable. The main result is that any complex number can be approximated by values of the Hurwitz zeta-function for arbitrary quadratic irrational parameters but with finite exceptions.
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