On p-adic multiple zeta and log gamma functions

On p -adic Hurwitz-type Euler zeta functions

“…Next we define the projection x for all x ∈ C × p , as was done by Kashio [9] and by Tangedal and Young in [23].…”

“…This integral was introduced by Volkenborn [24] and he also investigated many important properties of p-adic valued functions defined on the p-adic domain (see [24,25]). Recently, Tangedal and Young [23] defined p-adic multiple zeta and log gamma functions by using multiple Volkenborn integrals, and developed many of their properties.…”

“…In this paper, by using the fermionic p-adic integral I −1 ( f ) on Z p we define the p-adic Hurwitztype Euler zeta functions following Cohen's approach in [4,Chapter 11] and Tangedal-Young's approach in [23]. Our paper is organized as follows.…”

Explicit computation of Gross–Stark units over real quadratic fields

“…This allows us to apply his Theorem 6.2 [K, p. 121] with the special values of our functions in place of his. This leads to the second reason, namely, there is a very efficient formula (see [TY,Theorem 4.2]) for computing the p-adic counterpart G p,2 (x, (ω 1 , ω 2 )) when x, ω 1 , ω 2 satisfy (15), thus finally giving an effective means to compute ζ mp,p (0, C + ). We note that the formula in Theorem 4.2 of [TY] was directly inspired by the connection between formula (5) in the Introduction to Diamond's p-adic log gamma function G p ( x f ).…”

IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

“…Thus, the study of the symmetry properties of Bernoulli and Aopstol polynomials can be involved in the study of the symmetry properties of q-Bernoulli polynomials. The higher order q-Bernoull numbers and polynomials including their many applications in number theory, mathematical analysis and statistics have been extensively studied by several authors (see [9,14,24,27,28,30,33,34]). Recently, D. S. Kim [8] derived eight basic identities of symmetry in three variables related to the q-extension power sums and the q-Bernoulli polynomials, thus generalized Tuenter's classical identity (1.8) in various forms.…”