Probabilistic methods in the theory of the Riemann zeta-function

R. N. Boyarinov

Teoriâ veroâtnostej i ee primeneniâ, Tome 56 (2011) no. 2, pp. 209-223

Bibliographie

[1] Karatsuba A. A., Korolev M. A., “Argument dzeta-funktsii Rimana”, Uspekhi matem. nauk, 60:3 (2005), 41–96 | MR | Zbl

[2] Bohr N., Landau E., “Beiträge zur Theorie der Riemannschen Zetafunktion”, Math. Ann., 74:1 (1913), 3–30 | DOI | MR | Zbl

[3] Selberg A., “Contributions to the theory of the Riemann zeta-function”, Arch. Math. Naturvid., 48:5 (1946), 89–155 | MR | Zbl

[4] Ghosh A., “On Riemann's zeta-function — sign changes of $S(T)$”, Recent Progress in Analytic Number Theory (Durham, 1979), v. 1, Academic Press, New York, 1981, 25–46 | MR

[5] Karatsuba A. A., “O funktsii $S(t)$”, Izv. RAN, 60:5 (1996), 27–56 | MR | Zbl

[6] Korolev M. A., “Ob argumente dzeta-funktsii Rimana na kriticheskoi pryamoi”, Tr. MIAN, 239, 2002, 215–238

[7] Karatsuba A. A., Korolev M. A., “Povedenie argumenta dzeta-funktsii Rimana na kriticheskoi pryamoi”, Uspekhi matem. nauk, 61:3 (2006), 3–92

[8] Vaughan R. C., Wooley T. D., “On the distribution of generating functions”, Bull. Lond. Math. Soc., 30:2 (1998), 113–122 | DOI | MR | Zbl

[9] Korolev M. A., “Gipoteza Selberga o raspredelenii znachenii mnimykh chastei nulei dzeta-funktsii Rimana”, Dokl. RAN, 421:3 (2008), 308–311 | Zbl

[10] Boyarinov R. N., “O drobnykh momentakh sluchainykh velichin”, Dokl. RAN, 436:3 (2011), 299–301 | MR

[11] Boyarinov R. N., “O skorosti skhodimosti raspredelenii sluchainykh velichin”, Dokl. RAN, 435:3 (2010), 295–297 | Zbl

[12] Boyarinov R. N., “O skorosti skhodimosti k predelnomu raspredeleniyu”, Vestn. MGU, ser. 1, matem. mekh., 2011, no. 2, 20–27 | MR

[13] Boyarinov R. N., Chubarikov V. N., “O raspredelenii znachenii funktsii na posledovatelnosti Fibonachchi”, Dokl. RAN, 379:1 (2001), 9–11 | MR | Zbl

[14] Boyarinov R. N., “O raspredelenii znachenii dzeta-funktsii Rimana”, Dokl. RAN, 438:1 (2011), 14–16

[15] Mueller J., “On the Riemann zeta function $\zeta(s)$ — gaps between sign changes of $S(t)$”, Mathematika, 29:2 (1983), 264–269 | DOI | MR

[16] Korolev M. A., “Izmenenie znaka funktsii $S(t)$ na korotkikh promezhutkakh”, Izv. RAN, 69:4 (2005), 75–88 | MR | Zbl

[17] Boyarinov R. N., “Izmenenie znaka funktsii na korotkikh intervalakh”, Vestn. MGU, ser. 1, matem. mekh., 2010, no. 3, 51–53

[18] Boyarinov R. N., “O raspredelenii bolshikh znachenii argumenta dzeta-funktsii Rimana”, Vestn. MGU, ser. 1, matem. mekh., 2010, no. 6, 55–58

[19] Montgomery H. L., “The pair correlation of zeros of the zeta function”, Proc. Sympos. Pure Math., 24 (1973), 181–193 | MR | Zbl

[20] Fujii A., “On the distribution of the zeros of the Riemann zeta function in short intervals”, Bull. Amer. Math. Soc., 81:1 (1975), 139–142 | DOI | MR | Zbl

[21] Fujii A., “On the zeros of dirichlet $L$-functions. II”, Trans. Amer. Math. Soc., 267:1 (1981), 33–40 | MR | Zbl

[22] Cheer A. Y., Goldston D. A., “Simple zeros of the Riemann zeta-function”, Proc. Amer. Math. Soc., 118:2 (1993), 365–372 | DOI | MR | Zbl

[23] Conrey J. B., Ghosh A., Gonek S. M., “Simple zeros of the Riemann zeta-function”, Proc. Lond. Math. Soc., Ser. III, 76:3 (1998), 165–372 | MR

[24] Korolev M. A., “O kratnykh nulyakh dzeta-funktsii Rimana”, Izv. RAN, 70:3 (2006), 3–22

[25] Boyarinov R. N., “O nulyakh dzeta-funktsii Rimana bolshoi kratnosti”, Matem. zametki, 89:5 (2011), 652–657

[26] Fujii A., “On the difference between $r$ consecutive ordinates of the zeros of the Riemann zeta-function”, Proc. Japan Acad., 51:10 (1975), 741–743 | DOI | MR | Zbl

[27] Ivić A., “On small values of the Riemann zeta-function on the critical line and gaps between zeros”, Liet. Mat. Rink., 42:1 (2002), 25–36 | MR | Zbl

[28] Boyarinov R. N., “O bolshikh rasstoyaniyakh mezhdu posledovatelnymi nulyami dzeta-funktsii Rimana”, Diskret. matem., 22:3 (2010), 75–82