401-3113-68L Exponential Sums over Finite Fields
Semester | Herbstsemester 2018 |
Dozierende | E. Kowalski |
Periodizität | einmalige Veranstaltung |
Lehrsprache | Englisch |
Kurzbeschreibung | Exponential sums over finite fields arise in many problems of number theory. We will discuss the elementary aspects of the theory (centered on the Riemann Hypothesis for curves, following Stepanov's method) and survey the formalism arising from Deligne's general form of the Riemann Hypothesis over finite fields. We will then discuss various applications, especially in analytic number theory. |
Lernziel | The goal is to understand both the basic results on exponential sums in one variable, and the general formalism of Deligne and Katz that underlies estimates for much more general types of exponential sums, including the "trace functions" over finite fields. |
Inhalt | Examples of elementary exponential sums The Riemann Hypothesis for curves and its applications Definition of trace functions over finite fields The formalism of the Riemann Hypothesis of Deligne Selected applications |
Skript | Lectures notes from various sources will be provided |
Literatur | Kowalski, "Exponential sums over finite fields, I: elementary methods: Iwaniec-Kowalski, "Analytic number theory", chapter 11 Fouvry, Kowalski and Michel, "Trace functions over finite fields and their applications" |