Mean values of the logarithmic derivative of the Riemann zeta-function with applications to primes in short intervals

Journal fur die Reine und Angewandte Mathematik

Volumn 537, Issue , 2001, Pages 105-126

  Goldston, D A ^a   Gonek, S M ^b   Montgomery, H L ^c  

^a SAN JOSE STATE UNIVERSITY   (United States)

^b UNIVERSITY OF ROCHESTER   (United States)

^c UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035538598     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (14)

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2. H. Davenport, Multiplicative Number Theory, 2nd edition, revised by H. L. Montgomery, Springer, New York 1980.
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5. P. X. Gallagher and J. Mueller, Primes and zeros in short intervals, J. reine angew. Math. 303/304 (1978), 205-220.
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7. D. A. Goldston and S. M. Gonek, A note on the number of primes in short intervals, Proc. AMS 108 No. 3 (1990), 613-620.
8. D. A. Goldston and H. L. Montgomery, Pair correlation of zeros and primes in short intervals, Analytic Number Theory and Diophantine Problems, Birkhäuser, Boston, Mass. (1987), 183-203.
9. S. M. Gonek, An explicit formula of Landau and its applications to the theory of the zeta-function, in: A tribute to Emil Grosswald: Number theory and related analysis, AMS Contemp. Math. 143 (1993), 395-413.
10. H. L. Montgomery, The pair correlation of zeros of the zeta function, Proc. Sympos. Pure Math. 24, Amer. Math. Soc., Providence, R. I. (1973), 181-193.
11. J. H. Mueller, Arithmetic equivalent of essential simplicity of zeta zeros, Trans. Amer. Math. Soc 275 (1983), 175-183.
12. A. Selberg, On the normal density of primes in small intervals,and the difference between consecutive primes, Arch. Math. Naturvid. 47, No. 6 (1943), 87-105.
13. A. Selberg, On the remainder in the formula for N(T), the number of zeros of ζ(s) in the strip 0 < t < T, Avh. Norske Vid. Akad. Oslo. I 1 (1944), 27 pp.
14. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., revised by D. R. Heath-Brown, Clarendon, Oxford 1986.