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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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Analytic properties of the van der Geer- Schoof zeta function
by
Jeffrey C. Lagarias
AT&T Labs
Coauthors: Eric Rains (AT&T Labs)

G. van der Geer and R. Schoof recently developed an exact analogue of the Riemann-Roch theorem for number fields, using Arakelov divisors. This led them to define a two-variable zeta function LK(u, s) attached to an algebraic number field K, analogous to a two-variable zeta function for function fields proposed by R. Pellikaan. We consider the case K=Q, where for u = 1 one has LQ(1, s) is the Riemann zeta function with the usual gamma factors included. The talk will present various results on the analytic properties of this function, in particular on the number and location of zeros of LQ(u, s), for various values of u.

Date received: March 9, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadx-67.