2016
DOI: 10.1007/s00029-016-0233-2
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Fundamentals of p-adic multiple L-functions and evaluation of their special values

Abstract: Abstract. We construct p-adic multiple L-functions in several variables, which are generalizations of the classical Kubota-Leopoldt p-adic L-functions, by using a specific p-adic measure. Our construction is from the p-adic analytic side of view, and we establish various fundamental properties of these functions:

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Cited by 7 publications
(9 citation statements)
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“…. , s r ) ∈ N r , the associated Carlitz multiple polylogarithm (abbreviated as CMPL) and the Carlitz multiple star polylogarithm (abbreviated as CMSPL, compared with the terminology in [FKMT17]) are defined by the series…”
Section: Cmpls and Cmsplsmentioning
confidence: 99%
“…. , s r ) ∈ N r , the associated Carlitz multiple polylogarithm (abbreviated as CMPL) and the Carlitz multiple star polylogarithm (abbreviated as CMSPL, compared with the terminology in [FKMT17]) are defined by the series…”
Section: Cmpls and Cmsplsmentioning
confidence: 99%
“…Those results further motivates the construction of the theory of p-adic multiple L-functions. A double analogue of the Kubota-Leopoldt p-adic L-function was introduced in [13, Section 4], and then, a more general theory of p-adic multiple L-functions has been developed in [6].…”
Section: Holdsmentioning
confidence: 99%
“…Since L 2 (s 1 , s 2 ; a 1 , a 2 ; ω 1 , ω 2 ) can be written as a linear combination of functions of the form (4.5), it is sufficient to show a functional equation for (4.5). This can be done in a way similar to the proofs of Theorem 2.1 and Theorem 3.1 (see [13,Sections 5,6]). § 5.…”
Section: Holdsmentioning
confidence: 99%
“…In the present paper, we consider positive characteristic analogues of p-adic multiple L-functions ( [8]).…”
Section: Introductionmentioning
confidence: 99%
“…[11]). In [8], Furusho, Komori, Matsumoto and Tsumura constructed p-adic versions of multiple zeta functions called p-adic multiple L-functions. Their method of construction is a generalization of Koblitz's integral expressions of p-adic L-functions.…”
Section: Introductionmentioning
confidence: 99%