Simple zeros of the Riemann zeta-function

Authors:
A. Y. Cheer and D. A. Goldston

Journal:
Proc. Amer. Math. Soc. **118** (1993), 365-372

MSC:
Primary 11M26

DOI:
https://doi.org/10.1090/S0002-9939-1993-1132849-0

MathSciNet review:
1132849

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Abstract | References | Similar Articles | Additional Information

Abstract: Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25

**[1]**J. B. Conrey,*On the distribution of the zeros of the Riemann zeta-function*, Topics in Analytic Number Theory, University of Texas Press, Austin, TX, 1985, pp. 28-41. MR**804240****[2]**-,*More than two-fifths of the zeros of the Riemann zeta function are on the critical line*, J. Reine Angew. Math.**399**(1989), 1-26. MR**1004130 (90g:11120)****[3]**J. B. Conrey, A. Ghosh, D. Goldston, S. M. Gonek, and D. R. Heath-Brown,*Distribution of gaps between zeros of the zeta function*, Quart. J. Math. Oxford Ser. (2)**36**(1985), 43-51. MR**780348 (86j:11083)****[4]**J. B. Conrey, A. Ghosh, and S. M. Gonek,*Mean values of the Riemann zeta-function*, Number Theory, Trace Formulas and Discrete Groups (Symposium in Honor of Atle Selberg, Oslo, Norway, July 14-21, 1987), Academic Press, New York, 1989, pp. 185-199. MR**993316 (90h:11077)****[5]**P. X. Gallagher,*Pair correlation of zeros of the zeta function*, J. Reine Angew. Math.**362**(1985), 72-86. MR**809967 (87e:11101)****[6]**D. A. Goldston and H. L. Montgomery,*Pair correlation of zeros and primes in short intervals*, Analytic Number Theory and Diophantine Problems, Birkhaüser, Boston, MA, 1987, pp. 183-203. MR**1018376 (90h:11084)****[7]**J. van de Lune, H. J. J. te Riele, and D. T. Winter,*On the zeros of the Riemann zeta function in the critical strip*. IV, Math. Comp.**46**(1986), 667-681. MR**829637 (87e:11102)****[8]**H. L. Montgomery,*The pair correlation of zeros of the zeta function*, Proc. Sympos. Pure Math., vol. 24, Amer. Math. Soc., Providence, RI, 1973, pp. 181-193. MR**0337821 (49:2590)****[9]**-,*Distribution of zeros of the Riemann zeta function*, Proc. Internat. Congr. Math. Vancouver, 1974, pp. 379-381. MR**0419378 (54:7399)****[10]**A. M. Odlyzko,*On the distribution of spacings between zeros of the zeta function*, Math. Comp.**48**(1987), 273-308. MR**866115 (88d:11082)****[11]**-,*The*-*th zero of the Riemann zeta function and**million of its neighbors*(to appear).

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1132849-0

Article copyright:
© Copyright 1993
American Mathematical Society