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Small zeros of quadratic L-functions

Published online by Cambridge University Press:  17 April 2009

Ali E. Özlük  and
C. Snyder
Ali E. Özlük
Affiliation:
Department of Mathematics, University of Maine, Neville Hall Orono ME 04469 0122, United States of America
C. Snyder
Affiliation:
Department of Mathematics, University of Maine, Neville Hall Orono ME 04469 0122, United States of America
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Abstract

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We study the distribution of the imaginary parts of zeros near the real axis of quadratic L-functions. More precisely, let K(s) be chosen so that |K(1/2 ± it)| is rapidly decreasing as t increases. We investigate the asymptotic behaviour of

as D → ∞. Here denotes the sum over the non-trivial zeros p = 1/2 + iγ of the Dirichlet L-function L(s, χd), and χd = () is the Kronecker symbol. The outer sum is over all fundamental discriminants d that are in absolute value ≤ D. Assuming the Generalized Riemann Hypothesis, we show that for

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 2 , April 1993 , pp. 307 - 319
Copyright
Copyright © Australian Mathematical Society 1993

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