Abstract: In the 1980's, Greene introduced $_nF_{n-1}$ hypergeometric functions over finite fields using normalized Jacobi sums. The framework of his theory implies that these functions possess many properties that are analogous to those of the classical hypergeometric series studied by Gausz, Kummer and others. In this talk, we discuss the value distributions of certain ``simplest'' families of these hypergeometric functions. For the $_2F_1$ functions, the limiting distribution is semicircular, whereas the distribution for the $_3F_2$ functions is the Batman distribution.
This is joint work with Ken Ono and Hasan Saad.
New Results in Arithmetic Statistics
08.11.2022 15:15 - 16:45
Organiser:
Ch. Krattenthaler
Location:
Wiedner Hauptstrasze 8-10, Institut fuer Diskrete Mathematik und Geometrie, Dissertantenzimmer, 8. Stock, Turm A