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 (Austin, Tex., 1982) Univ. Texas Press, Austin, TX, 1985, pp. 28–41. MR**804240****[2]**J. B. Conrey,*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**, https://doi.org/10.1515/crll.1989.399.1**[3]**J. B. Conrey, A. Ghosh, D. Goldston, S. M. Gonek, and D. R. Heath-Brown,*On the distribution of gaps between zeros of the zeta-function*, Quart. J. Math. Oxford Ser. (2)**36**(1985), no. 141, 43–51. MR**780348**, https://doi.org/10.1093/qmath/36.1.43**[4]**J. B. Conrey, A. Ghosh, and S. M. Gonek,*Mean values of the Riemann zeta-function with application to the distribution of zeros*, Number theory, trace formulas and discrete groups (Oslo, 1987) Academic Press, Boston, MA, 1989, pp. 185–199. MR**993316****[5]**P. X. Gallagher,*Pair correlation of zeros of the zeta function*, J. Reine Angew. Math.**362**(1985), 72–86. MR**809967**, https://doi.org/10.1515/crll.1985.362.72**[6]**Daniel A. Goldston and Hugh L. Montgomery,*Pair correlation of zeros and primes in short intervals*, Analytic number theory and Diophantine problems (Stillwater, OK, 1984) Progr. Math., vol. 70, Birkhäuser Boston, Boston, MA, 1987, pp. 183–203. MR**1018376****[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), no. 174, 667–681. MR**829637**, https://doi.org/10.1090/S0025-5718-1986-0829637-3**[8]**H. L. Montgomery,*The pair correlation of zeros of the zeta function*, Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 181–193. MR**0337821****[9]**Hugh L. Montgomery,*Distribution of the zeros of the Riemann zeta function*, Proceedings of the International Congress of Mathematicians (Vancouver, B. C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 379–381. MR**0419378****[10]**A. M. Odlyzko,*On the distribution of spacings between zeros of the zeta function*, Math. Comp.**48**(1987), no. 177, 273–308. MR**866115**, https://doi.org/10.1090/S0025-5718-1987-0866115-0**[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