Geodesic
The Density of Zeros of Dirichlet's L-Functions
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 231-240

Voir la notice de l'article provenant de la source Cambridge University Press

Let L(s, χ) be a Dirichlet L-function and let N(σ, T, χ) denote the number of zeros ρ of L(s, χ), counted according to multiplicity, in the rectangle σ ≦ Re(ρ) ≦ 1, |Im(ρ)| ≦ T, (T ≦ 1). In this paper we shall prove several new estimates for the sum where Σ* denotes summation over primitive characters only. These estimates will all be of the type (1) where denotes any fixed positive quantity. 
Heath-Brown, D. R. The Density of Zeros of Dirichlet's L-Functions. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 231-240. doi: 10.4153/CJM-1979-024-0
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[1] 1. Huxley, M. N., On the difference between consecutive primes, Invent. Math.. 15 (1972), 164–170. Google Scholar

[2] 2. Huxley, M. N., Large values of Dirichlet polynomials, III, Acta Arith.. 26 (1974), 435–444. Google Scholar

[3] 3. Huxley, M. N., An imperfect hybrid zero-density theorem, J. London Math. Soc, (2). 13 (1976), 53–56. Google Scholar

[4] 4. Ingham, A. E., On the difference between consecutive primes, Quart. J. Math. Oxford Ser.. 8 (1937), 255–266. Google Scholar

[5] 5. Jutila, M., On a density theorem of H. L. Montgomery for L-functions, Ann. Acad. Sci. Fenn. Ser. A I (1972), No. 520. Google Scholar

[6] 6. Jutila, M., Zero-density estimates for L-functions, Acta. Arith. 32 (1977), 55–62. Google Scholar

[7] 7. Montgomery, H. L., Topics in multiplicative number theory (Springer, Berlin, 1971). Google Scholar

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