Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-31T10:19:15.589Z Has data issue: false hasContentIssue false
  • English
  • Français

The Density of Zeros of Dirichlet's L-Functions

Published online by Cambridge University Press:  20 November 2018

D. R. Heath-Brown
D. R. Heath-Brown*
Affiliation:
Trinity College, Cambridge, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 231 - 240
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Huxley, M. N., On the difference between consecutive primes, Invent. Math.. 15 (1972), 164–170.Google Scholar
2. Huxley, M. N., Large values of Dirichlet polynomials, III, Acta Arith.. 26 (1974), 435–444.Google Scholar
3. Huxley, M. N., An imperfect hybrid zero-density theorem, J. London Math. Soc, (2). 13 (1976), 53–56.Google Scholar
4. Ingham, A. E., On the difference between consecutive primes, Quart. J. Math. Oxford Ser.. 8 (1937), 255–266.Google Scholar
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. Jutila, M., Zero-density estimates for L-functions, Acta. Arith. 32 (1977), 55–62.Google Scholar
7. Montgomery, H. L., Topics in multiplicative number theory (Springer, Berlin, 1971).Google Scholar