Zeta and Related Functions
نویسنده
چکیده
Riemann Zeta Function 602 25.2 Definition and Expansions . . . . . . . . 602 25.3 Graphics . . . . . . . . . . . . . . . . . . 603 25.4 Reflection Formulas . . . . . . . . . . . . 603 25.5 Integral Representations . . . . . . . . . 604 25.6 Integer Arguments . . . . . . . . . . . . 605 25.7 Integrals . . . . . . . . . . . . . . . . . . 606 25.8 Sums . . . . . . . . . . . . . . . . . . . 606 25.9 Asymptotic Approximations . . . . . . . . 606 25.10 Zeros . . . . . . . . . . . . . . . . . . . 606
منابع مشابه
A certain family of series associated with the Zeta and related functions
The history of problems of evaluation of series associated with the Riemann Zeta function can be traced back to Christian Goldbach (1690–1764) and Leonhard Euler (1707–1783). Many di¤erent techniques to evaluate various series involving the Zeta and related functions have since then been developed. The authors show how elegantly certain families of series involving the Zeta function can be eval...
متن کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کاملBounds for Zeta and Related Functions
Sharp bounds are obtained for expressions involving Zeta and related functions at a distance of one apart. Since Euler discovered in 1736 a closed form expression for the Zeta function at the even integers, a comparable expression for the odd integers has not been forthcoming. The current article derives sharp bounds for the Zeta, Lambda and Eta functions at a distance of one apart. The methods...
متن کاملPartial Epstein zeta functions on binary linear codes and their functional equations
In this paper, partial Epstein zeta functions on binary linear codes, which are related with Hamming weight enumerators of binary linear codes, are newly defined. Then functional equations for those zeta functions on codes are presented. In particular, it is clarified that simple functional equations hold for partial Epstein zeta functions on binary linear self-dual codes.
متن کاملOn the Theory of Zeta-functions and L-functions
In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet’s L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we ...
متن کاملar X iv : d g - ga / 9 70 10 08 v 3 2 1 A pr 1 99 7 Geometric zeta - functions on p - adic groups ∗
We generalize the theory of p-adic geometric zeta functions of Y. Ihara and K. Hashimoto to the higher rank case. We give the proof of rationality of the zeta function and the connection of the divisor to group cohomology, i.e. the p-adic analogue of the Patterson conjecture. Introduction. In [13] and [14] Y. Ihara defined geometric zeta functions for the group PSL2. This was the p-adic counter...
متن کامل