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References:
[1] AYOUB R.: Euler and the zeta function. Amer. Math. Monthlу 81 (1974), 1067-1086. MR 0360116 | Zbl 0293.10001
[2] BACKLUND R.: Sur les zéros de la fonction $\zeta(s)$ de Riemann. Comptes Rendus 158 (1914), 1979-1981.
[3] BERNOULLI J.: Ars Conjectandi. Basel, 1713. Zbl 0957.01032
[4] BRENT R. P.-VAN DE LUNE J.-TE RIELE H. J. J.-WINTER D. T.: On the zeros of the Riemann zeta function in the critical strip. II. Math. Comp. 39 (1982), 681-688. MR 0669660
[5] DE BRUIJN N. G.: Asymptotic Methods in Analysis. North-Holland Publ., Amsterdam, 1958. Zbl 0082.04202
[6] CHOI J.-SRIVASTAVA H. M.: Series Associated with the Zeta and Related Functions. Kluwer Academic Pub., Dordrecht-Boston-London, 2001. MR 1849375 | Zbl 1160.11339
[7] DAVENPORT H.: Multiplicative Number Theory. (1st ed.) Markham Publ. Co., Chicago, 1967. MR 0217022 | Zbl 0159.06303
[8] DIRICHLET P. G. L.: Sur l'usage des series infinies dans la théorie des nombres. J. Reine Angew. Math. 18 (1838), 257-274.
[9] EDWARDS H. M.: Riemann's Zeta Function. Academic Press, San Diego, 1974. Zbl 0315.10035
[10] EULER L.: De progressionibus transcendentibus. Comm. Acad. Sci. Petrop. 5 (1730), 36-57.
[11] EULER L.: Variae observationes circa series infinitas. Comm. Acad. Sci. Petrop. 9 (1737), 222-236.
[12] EULER L.: Introductio in Analysin Infinitorum. (Chapter 15), Lausanne, 1748. Zbl 0967.01027
[13] EULER L.: Novi Comment. Acad. Petrop. 4 (1771), 105. Zbl 1221.65025
[14] GROSSWALD E.: Topics from the Theory of Numbers. The Macmillan Co., New York, 1966. MR 0228408 | Zbl 0158.29501
[15] HADAMARD J.: Sur la distribution des zéros de la fonction $\zeta(s)$ et ses consequences arithmétiques. Bull. Soc Math. France 24 (1896), 199-220. MR 1504264
[16] HARDY G. H.-LITTLEWOOD J. E.: The zeros of the Riemann zeta function on the critical line. Math. Z. 10 (1921), 283-317. MR 1544477
[17] IVIC A.: The Riemann Zeta-Function (The Theory of the Riemann Zeta-Function with Applications). A Wiley-Interscience, New York, 1985. MR 0792089 | Zbl 0556.10026
[18] KARASTUBA A. A.-VORONIN S. M.: The Riemann Zeta-Function. de Gruyter Exp. Math., de Gruyter, Berlin, 1992. MR 1183467
[19] LANG S.: Complex Analysis. (4th ed.). Grad. Texts in Math. 103, Springer-Verlag, New York, 1999. MR 1659317 | Zbl 0933.30001
[20] LINDELÖF E.: Quelques remarques sur la croissance de la fonction $\zeta(s)$. Bull. Sci. Math. 32 (1908), 341-356.
[21] VAN DE LUNE J.-TE RIELE H. J. J.: On the zeros of the Riemann zeta function in the critical strip. HI, Math. Comp. 41 (1983), 759-767. MR 0717719
[22] MELLIN H.: Eine Formel fÜr den Logarithmus transcendenter Funktionen von endlichem Geschlecht. Acta Math. 25 (1902), 165-183. MR 1554942
[23] MERTENS F.: Über eine Eigenschaft der Riemann'schen $\zeta$-Function. Sitzungsberichte Akad. Wiss. Wien. Math.-Natur. Kl. 107 (1898), 1429-1434.
[24] MONTGOMERY H. L.: The pair correlation of zeros of the zeta function. In: Analytic Number Theory, (Proc Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), Amer. Math. Soc, Providence, RI, 1973, pp. 181-193. MR 0337821
[25] MURTY M. R.: Problems in Analytic Number Theory. Grad. Texts in Math. 206, Springer, New York, 2001. MR 1803093 | Zbl 1190.11001
[26] NEWMAN D. J.: Simple analytic proof of the prime number theorem. Amer. Math. Monthly 87 (1980), 693-696. MR 0602825 | Zbl 0444.10033
[27] ODLYZKO A. M.: The $1022$-nd zero of the Riemann zeta function. In: Dynamical, Spectral, and Arithmetic Zeta Functions. AMS special session, San Antonio, TX, USA, January 15-16, 1999. Contemp. Math. 290, Amer. Math. Soc, Providence, RI, 2001, pp. 139-144. MR 1868473
[28] ODLYZKO A. M.-SCHOENHAGE A.: Fast algorithms for multiple evaluations of the Riemann zeta function. Trans. Amer. Math. Soc. 309 (1988), 797-809. MR 0961614 | Zbl 0706.11047
[29] RIEMANN B.: Über die Anzahl der Primzahlen unter einer gegebenen Grosse (1859). Collected Works, Teubner, Leipzig, 1892.
[30] SELBERG A.: The zeta-function and the Riemann Hypothesis. In: Proc. Skand. Math. Kongr., Kobenhavn, 1947, pp. 187-200. MR 0019676 | Zbl 0030.05003
[31] STIELTJES T. J.: Sur le developpement de $\log\Gamma(a)$. J. Math. Pures Appl. (9) 5 (1889), 425-444.
[32] STIRLING J.: Methodus Differential. London, 1730.
[33] SWINNERTON-DYER H. P. F.: A Brief Guide to Algebraic Number Theory. London Math. Soc. Stud. Texts 50, Univ. Press, Cambridge, 2001. MR 1826558 | Zbl 0963.11001
[34] TITCHMARSH E.: The Theory of the Riemann Zeta-Function. (2nd ed., revised by D. R. Heath-Brown), Oxford Univ. Press, Oxford, 1986. MR 0882550 | Zbl 0601.10026
[35] DE LA VALLEE-POUSSIN, CH.: Recherches analytiques sur la theorie des nombres. Ann. Soc. Sci. Bruxelles 20 (1896), 183-256.
[36] WALFISZ A.: Weylsche Exponentialsummen in der Neueren Zahlentheorie. VEB Deutcher Verlag der Wiss., Berlin, 1963. MR 0220685 | Zbl 0146.06003
[37] WHITTAKER E. T.-WATSON G. N.: A Course of Modern Analysis. (An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions), Cambridge Univ. Press, Cambridge, 1927. MR 1424469
[38] ZAGIER D.: Newman's short proof of the prime number theorem. Amer. Math. Monthly 104 (1997), 705-708. MR 1476753 | Zbl 0887.11039
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