关于举行韩国庆南大学Kim Min-Soo 副教授学术报告会的通知

报告题目：On p-adic multiple Barnes-Euler zeta functions and the corresponding log gamma functions

报 告 人：Kim Min-Soo 副教授（韩国庆南大学）
报告时间：2018年2月27日（星期二）下午4:00-5:00
邀 请 人：胡甦 副教授
报告地点：四号楼4318室
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                                                              数学学院
                                                           2018年02月26日

报告摘要：Suppose that $\omega_1,\ldots,\omega_N$ are positive real numbers and $x$ is a complex number with positive real part.The multiple Barnes-Euler zeta function $\zeta_{E,N}(s,x;\bar\omega)$ with parameter vector $\bar\omega=(\omega_1,\ldots,\omega_N)$ is defined as a deformation of  the Barnes multiple  zeta function as follows $$\zeta_{E,N}(s,x;\omega_1,\ldots,\omega_N)=\sum_{t_1=0}^\infty\cdots\sum_{t_N=0}^\infty\frac{(-1)^{t_1+\cdots+t_N}}{(x+\omega_1t_1+\cdots+\omega_Nt_N)^s}.$$ In this work, based on the fermionic $p$-adic integral, we define the $p$-adic analogue of multiple Barnes-Euler zeta function $\zeta_{E,N}(s,x;\bar\omega)$ which we denote by $\zeta_{p,E,N}(s,x;\bar\omega).$  We prove several properties of  $\zeta_{p,E,N}(s,x; \bar\omega)$, including the convergent Laurent series expansion, the distribution formula, the difference equation, the reflection functional equation and the derivative formula.By computing the values of this kind of $p$-adic zeta function at nonpositive integers, we show that it interpolates the higher order Euler polynomials  $E_{N,n}(x;\bar\omega)$ $p$-adically. Furthermore, we define the corresponding $p$-adic multiple log gamma function $G_{p,E,N}(x,\bar\omega)$ as the derivative of  $\zeta_{p,E,N}(s,x; \bar\omega)$ at $s=0$. We also show  that the $p$-adic  log gamma function $G_{p,E, N}(x;\bar\omega)$ has an integral representation by the multiple fermionic $p$-adic integral,  and it  satisfies   the distribution formula, the difference equation, the reflection functional equation, the derivative formula  and also the Stirling's series expansions.