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Small zeros of quadratic \(L\)-functions. (English) Zbl 0777.11031
Various authors have shown that the zeros of Dirichlet \(L\)-functions close to the real axis have a significant bearing on such topics as the distribution of primes among residue classes \(\pmod q\) and the class numbers of non-real quadratic fields. The authors investigate the distribution of the imaginary parts of zeros of quadratic \(L\)-functions near the real axis by determining the asymptotic behavior of a certain sum over fundamental discriminants which are absolutely \(\leq D\) as \(D\to\infty\). The results assume the Generalized Riemann Hypothesis.

11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
Full Text: DOI
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