Bulletin of the Australian Mathematical Society

Research Article

Small zeros of quadratic L-functions

Ali E. Özlüka1 and C. Snydera1

a1 Department of Mathematics, University of Maine, Neville Hall Orono ME 04469 0122, United States of America


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 S0004972700012545_inline1 denotes the sum over the non-trivial zeros p = 1/2 + of the Dirichlet L-function L(s, χd), and χd = (S0004972700012545_inline2) is the Kronecker symbol. The outer sum S0004972700012545_inline3 is over all fundamental discriminants d that are in absolute value ≤ D. Assuming the Generalized Riemann Hypothesis, we show that for


(Received April 14 1992)