Asymptotic behaviour of some infinite products involvingprime numbers

 Access to full text

 Full (PDF)

1. [1] M. Car, Factorisation dans $F_q\left[X\right]$, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), 147-150. Zbl0492.12010
2. [2] A. Erdélyi, Higher Transcendental Functions, Vol. I, Krieger, Malabar, Fla., 1953. Zbl0051.30303
3. [3] M. A. Evgrafov, Asymptotic Estimates and Entire Functions, Gordon and Breach, New York, 1961 (translated from Russian by A. L. Shields). 
4. [4] P. Flajolet, X. Gourdon, and P. Dumas, Mellin transforms and asymptotics: harmonic sums, Theoret. Comput. Sci. 144 (1995), 3-58. Zbl0869.68057
5. [5] P. Flajolet and M. Soria, Gaussian limiting distributions for the number of components in combinatorial structures, J. Combin. Theory Ser. A 53 (1990), 165-182. Zbl0691.60035
6. [6] D. Hensley, The distribution of round numbers, Proc. London Math. Soc. (3) 54 (1987), 412-444. Zbl0588.10047
7. [7] A. Hildebrand and G. Tenenbaum, On the number of prime factors of an integer, Duke Math. J. 56 (1988), 471-501. Zbl0655.10036
8. [8] H.-K. Hwang, Théorèmes limites pour les structures combinatoires et les fonctions arithmétiques, Thèse, Ecole Polytechnique, 1994. 
9. [9] A. Ivić, The Riemann Zeta-Function, Wiley, New York, 1985. Zbl0556.10026
10. [10] A. Knopfmacher, J. Knopfmacher, and R. Warlimont, 'Factorisatio numerorum' in arithmetical semigroups, Acta Arith. 61 (1992), 327-336. Zbl0772.11038
11. [11] J. Knopfmacher, Abstract Analytic Number Theory, North-Holland, Amsterdam, 1975. Zbl0322.10001
12. [12] J. Knopfmacher, Analytic Arithmetic of Algebraic Function Fields, Lecture Notes in Pure and Appl. Math. 50, Dekker, New York, 1979. Zbl0411.10001
13. [13] K. K. Norton, On the frequencies of large values of divisor functions, Acta Arith. 68 (1994), 219-244. Zbl0816.11047
14. [14] G. J. Rieger, Zum Teilerproblem von Atle Selberg, Math. Nachr. 30 (1965), 181-192 
15. [15] L. G. Sathe, On a problem of Hardy and Ramanujan on the distribution of integers having a given number of prime factors, I, II, III, IV, J. Indian Math. Soc. 17 (1953), 63-141; 18 (1954), 27-81. Zbl0051.28008
16. [16] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87. 
17. [17] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Institut Elie Cartan, Université de Nancy I, Nancy, 1990. 
18. [18] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, 1951; 2nd ed., revised and edited by D. R. Heath-Brown, Oxford Sci. Publ., Clarendon Press, Oxford, 1986. Zbl0042.07901
19. [19] R. Warlimont, Arithmetical semigroups IV: Selberg's analysis, Arch. Math. (Basel) 60 (1993), 58-72. Zbl0809.11058
20. [20] R. Wong, Asymptotic Approximations of Integrals, Academic Press, Boston, 1989. Zbl0679.41001