Numerical treatment of analytic continuation with Multiple-precision arithmetic
نویسندگان
چکیده
منابع مشابه
Chern-simons Theory, Analytic Continuation and Arithmetic
The purpose of the paper is to introduce some conjectures regarding the analytic continuation and the arithmetic properties of quantum invariants of knotted objects. More precisely, we package the perturbative and nonperturbative invariants of knots and 3-manifolds into two power series of type P and NP, convergent in a neighborhood of zero, and we postulate their arithmetic resurgence. By the ...
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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.
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 2007
ISSN: 0385-4035
DOI: 10.14492/hokmj/1272848036