Desingularization of complex multiple zeta-functions
نویسندگان
چکیده
منابع مشابه
Multiple finite Riemann zeta functions
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some q-series identity for proving the zeta function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite cou...
متن کاملAnalytic Continuation of Multiple Zeta Functions
In this paper we shall define the analytic continuation of the multiple (Euler-Riemann-Zagier) zeta functions of depth d: ζ(s1, . . . , sd) := ∑ 0 1 and ∑d j=1 Re (sj) > d. We shall also study their behavior near the poles and pose some open problems concerning their zeros and functional equations at the end.
متن کاملAnalytic continuation of multiple Hurwitz zeta functions
We use a variant of a method of Goncharov, Kontsevich, and Zhao [Go2, Z] to meromorphically continue the multiple Hurwitz zeta function ζd(s; θ) = ∑ 0<n1<···<nd (n1 + θ1) −s1 · · · (nd + θd)d , θk ∈ [0, 1), to C, to locate the hyperplanes containing its possible poles, and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s; θ).
متن کاملOn Functions of Arakawa and Kaneko and Multiple Zeta Functions
We study for s ∈ N the functions ξk(s) = 1 Γ(s) R ∞ 0 t et−1 Lik(1−e )dt, and more generally ξk1,...,kr (s) = 1 Γ(s) R ∞ 0 t et−1 Lik1,...,kr (1 − e )dt, introduced by Arakawa and Kaneko [2] and relate them with (finite) multiple zeta functions, partially answering a question of [2]. In particular, we give an alternative proof of a result of Ohno [8].
متن کاملMultiple q-zeta functions and multiple q-polylogarithms
For every positive integer d we define the q-analog of multiple zeta function of depth d and study its properties, generalizing the work of Kaneko et al. who dealt with the case d = 1. We first analytically continue it to a meromorphic function on C with explicit poles. In our Main Theorem we show that its limit when q ↑ 1 is the ordinary multiple zeta function. Then we consider some special va...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: American Journal of Mathematics
سال: 2017
ISSN: 1080-6377
DOI: 10.1353/ajm.2017.0002