Seminar by Peter Roquette (Prof. Emeritus, Univ. of Heidelberg)

 The Riemann Hypothesis in Characteristic p, Its Origin and Development

by Peter Roquette  (University of Heidelberg)

Every curve defined over a finite field leads to a zeta function whose
properties reflect the arithmetic of the curve. In analogy to the
classical case the roots of these zeta functions were conjectured to have
real part 1/2. This conjecture was first formulated by Artin in a letter
to Herglotz (1921) in the case of hyperelliptic curves.

In the talk I will describe the first attempts by Hasse who proved the
R.H. for ellitpic curves and, jointly with Davenport, for curves of Fermat
type (1933). Then I will report on the further activities mainly by Hasse,
Deuring and Weil who finally succeeded with the proof for arbitrary curves
(1941). The talk will be based largely on letters which were exchanged
between the active mathematicians during that time.

Date: November 12, Friday
Time: 15:00
Place: Sabanci University, Karakoy Communication Center,
         

All interested are welcome. Tea will be served after 14:30. Please contact Alev Topuzoğlu (alev@sabanciuniv.edu) for further information.