关于一个数论函数的导数及应用

Kanemitsu教授给出了欧拉求和函数的推广公式Lu(x,a)=0n相似文献   

A generalization of the riemann zeta-function

A generalization of the Riemann zeta-function which has the form

The Universality of Zeta-Functions

The first part of the paper contains a survey on the universality of zeta-functions. Zeta-functions with Euler's product as well as zeta-functions without Euler's product are discussed. Also, the joint universality theorems are considered. In the second part of the paper the universality of zeta-functions of finite Abelian groups of rank 3 is proved.     

On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

Approximation of the Lerch Zeta-Function

We consider uniform in parameters approximations of the Lerch zeta-function by Dirichlet polynomials. It allows us to obtain uniform in parameters bounds in the critical strip.     

Value distribution of the Lerch zeta-function with algebraic irrational parameter. IV

We obtain a joint limit theorem in the space of analytic functions for Lerch zeta-functions with algebraic irrational parameter. The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-81/09.     

Large gaps between consecutive zeros of the Riemann zeta-function

Combining the amplifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist infinitely many consecutive gaps greater than 3.033 times the average spacing.     

Cyclic sum of certain parametrized multiple series

In the present paper, we prove the cyclic sum formulas for certain parametrized multiple series.     

On Statistical Properties of the Lerch Zeta-Function. II

A discrete limit theorem for the Lerch zeta-function with an integer parameter in the space of meromorphic functions is proved.     

On some slowly convergent series involving the Hurwitz zeta-function

We shall extract the essence of the Adamchik–Srivastava generating function method (Analysis (Munich) 18 (1998) 131) by proving the most far-reaching Ramanujan–Yoshimoto formula and by showing that some of the results stated in Srivastava and Choi (Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001) are simple consequences of the above-mentioned formula.