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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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\Omega results for \Delta(x, n) = \sum'n < xN 1 - x j(N) and the non-vanishing of L(1, \chi)
by
Paolo Codecà
Dipartimento di Matematica - Università di Ferrara- Via Machiavelli 35 - 44100 Ferrara - ITALY
Coauthors: Mohan Nair (University of Glasgow, U.K.)

The function \Delta(x, N) as defined in the title has been studied by several authors and some \Omega and O results are known. We consider the special case in which all the prime numbers p/N belong to fixed residue classes mod q, where q is also a prime. In this case we prove very strong \Omega results for \Delta(N)=supx|\Delta(x, N)| related to the non-vanishing of \L(1, \chi), where \chi is a character mod q.

Date received: March 14, 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-94.