论文信息 - Some remarks on the Riemann zeta distribution

Some remarks on the Riemann zeta distribution

The Riemann zeta function ζ(z) = ∑∞ n=1 1 nz , where z = σ+it ∈ C, plays an important role in connection with the distribution of primes. A probabilistically pleasant fact is that the zeta function, as a function of t, properly normalized, is a characteristic function, the distribution of which is compound Poisson. This property is exploited and some facts from analytic number theory are (re)established.

Allan Gut | A. Gut

[1] Gérald Tenenbaum. An elementary proof of the prime number theorem , 2000 .

[2] K. Chung,et al. Limit Distributions for Sums of Independent Random Variables. , 1955 .

[3] D. R. Heath-Brown,et al. The Theory of the Riemann Zeta-Function , 1987 .

[4] E. Wright,et al. An Introduction to the Theory of Numbers , 1939 .

[5] Robert H. Bowmar. Limit theorems for sums of independent random variables , 1962 .

[6] G. Hardy,et al. An Introduction to the Theory of Numbers , 1938 .

[7] T. Apostol. Introduction to analytic number theory , 1976 .

[8] A. Wintner,et al. Distribution functions and the Riemann zeta function , 1935 .

[9] D. Applebaum. Lévy Processes and Stochastic Calculus: Preface , 2009 .

[10] G. D. Lin,et al. The Riemann zeta distribution , 2001 .

[11] A. Gut. Probability: A Graduate Course , 2005 .