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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.

MSC:
11M26 Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses
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[1] DOI: 10.1007/BF01303260 · Zbl 0431.10027 · doi:10.1007/BF01303260
[2] Bellman, Analytic number theory, an introduction (1980) · Zbl 0448.10001
[3] Ayoub, An introduction to the analytic theory of numbers 10 (1963) · Zbl 0128.04303
[4] DOI: 10.2307/2005484 · Zbl 0301.10035 · doi:10.2307/2005484
[5] DOI: 10.2307/2002800 · Zbl 0097.03001 · doi:10.2307/2002800
[6] DOI: 10.1016/0022-314X(82)90030-0 · Zbl 0489.10042 · doi:10.1016/0022-314X(82)90030-0
[7] Montgomery, Acta Arith. 24 pp 529– (1974)
[8] Ellison, Prime numbers (1985)
[9] Davenport, Multiplicative number theory (1980) · Zbl 0453.10002 · doi:10.1007/978-1-4757-5927-3
[10] Chebysev, Bull. Classe Phys. de l’Acad. Imp. Sciences St. Petersburg 11 pp 208– (1853)
[11] Turán, On a new method of analysis and its applications (1984) · Zbl 0544.10045
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