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201405.1504v3 Real zeros of Hurwitz-Lerch zeta and Hurwitz-Lerch type of Euler-Zagier double zeta functions.pdf
- Let 0<a≤1, s,z∈C and 0<|z|≤1. Then the Hurwitz-Lerch zeta function is defined by Φ(s,a,z):=∑∞n=0zn(n+a)−s when σ:=R(s)>1. In this paper, we show that the Hurwitz zeta function ζ(σ,a):=Φ(σ,a,1) does not vanish for all 0<σ<1 if and only if a≥1/2. Moreover, we prove that Φ(σ,a,z)≠0 for all 0<σ<1 and 0<a≤1 when z≠1. Real zeros of Hurwitz-Lerch type of Euler-Zagier double zeta functions are studied as well.
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201005.4712v2 The Lerch Zeta Function I. Zeta Integrals.pdf
- This is the first of four papers that study algebraic and analytic structures associated to the Lerch zeta function. This paper studies "zeta integrals" associated to the Lerch zeta function using test functions, and obtains functional equations for them. Special cases include a pair of symmetrized four-term functional equations for combinations of Lerch zeta functions, found by A. Weil, for real parameters (a,c) with 0< a, c< 1. It extends these functions to real a, and c, and studies limiting cases of these functions where at least one of a and c takes the values 0 or 1. A main feature is that as a function of three variables (s, a, c), with a, c being real variables, the Lerch zeta function has discontinuities at integer values of a and c. For fixed s, the function is discontinuous on part of the boundary of the closed unit square in the (a,c)-variables, and the location and nature of these discontinuities depend on the real part of s. Analysis of this behavior
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Heritable genetic variation via mutation-selection balance Lerch´s zeta meets the abdominal bristle.pdf
- Heritable genetic variation via mutation-selection balance Lerch´s zeta meets the abdominal bristle
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Riemann, Hurwitz and Hurwitz-Lerch Zeta Functions and Associated Series and Integrals.pdf
- Riemann, Hurwitz and Hurwitz-Lerch Zeta Functions and Associated Series and Integrals
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201404.4758v2 Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers.pdf
- We study analytic properties of multiple zeta-functions of generalized Hurwitz-Lerch type. First, as a special type of them, we consider multiple zeta-functions of generalized Euler-Zagier-Lerch type and investigate their analytic properties which were already announced in our previous paper. Next we give `desingularization´ of multiple zeta-functions of generalized Hurwitz-Lerch type, which include those of generalized Euler-Zagier-Lerch type, the Mordell-Tornheim type, and so on. As a result, the desingularized multiple zeta-function turns out to be an entire function and can be expressed as a finite sum of ordinary multiple zeta-functions of the same type. As applications, we explicitly compute special values of desingularized double zeta-functions of Euler-Zagier type. We also extend our previous results concerning a relationship between p-adic multiple L-functions and p-adic multiple star polylogarithms to more general indices with arbitrary (not necessarily all positive
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some properties of the lerch family of discrete distributions.pdf
- some properties of the lerch family of discrete distributions
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Certain families of series associated with the Hurwitz-Lerch Zeta function.pdf
- Certain families of series associated with the Hurwitz–Lerch Zeta function
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Evaluation of series with Hurwitz and Lerch zeta function coefficients by using Hankel contour integrals.pdf
- Evaluation of series with Hurwitz and Lerch zeta function coefficients by using Hankel contour integrals
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201005.4967v2 The Lerch Zeta Function II. Analytic Continuation.pdf
- This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables. We that it is well defined as a multivalued function on the manifold M equal to C^3 with the hyperplanes corresponding to integer values of the two variables a and c removed. We show that it becomes single valued on the maximal abelian cover of M. We compute the monodromy functions describing the multivalued nature of this function on M, and determine various of their properties
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向豆丁求助：有没有lerch?
