Title of the course: Zeta Functions and the Heisenberg Group
Instructor: Dr. E. Mehmet Kıral
Institution: Sophia University
Dates: 22-28 July 2019
Prerequisites: Enough mathematical maturity to not be dismayed by seeing a Fourier transform, or hearing the phrase representation theory. We can define any desired term, but you should be comfortable with not necessarily knowing the whole theory that is behind them with full rigour.
Although no particular knowledge is absolutely necessary, it is a reasonable assumption that if ALL of the following phrases are completely new to you, then you would have a difficult time trying to follow the lectures (some new words is ok): Square integrable functions, Hilbert Space, Unitary Operator, Unitary Representation of a group, Riemann Zeta function, Functional Equation, Gamma function, holomorphic function (analytic continuation), Matrix Group, Diagonalization.
Level: Graduate, advanced undergraduate
Abstract: I would like to emphasize the role of harmonic analysis in the functional equations of the Riemann zeta function, the Hurwitz zeta functions and other L-functions. The Fourier transform and its relation to the functional equation is encoded in the representation theory of the Heisenberg group.
Further topics at the intersection of number theory and harmonic analysis can be discussed.
Language: TR, EN