On a Dirichlet series associated with a polynomial
On a Dirichlet series associated with a polynomial
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关于与多项式相关的狄利克雷级数
DOI：
10.1090/s0002-9939-1990-1037206-0
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发表时间：
1990
期刊：
影响因子：
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通讯作者：
M. Eie
中科院分区：
文献类型：
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作者：
M. Eie
设P（x）k Hk=（x +3 J）是一个具有真实的系数的多项式，ReJi > -I（j = 1，. k）。定义与多项式P（x）相关的zeta函数Zp（s）为00 Zp（s）= 1 Res > I/k。ZP（n）s' ZP（s）是全纯的，Res > 1/k，且在全复s平面上解析延拓，只在s = j/k（j = 1，0，-1，-2，-3，.）..），而不是非正整数。本文给出了对任意非负整数m，Zp（-m）的显式值，Zp（s）在s = 1/k时的渐近公式，Z4（0）的值及其在椭圆算子行列式中的应用.
Let P(x) k Hk= (x + 3J) be a polynomial with real coefficients and ReJi > -I (j = 1, ... k) . Define the zeta function Zp(s) associated with the polynomial P(x) as 00 Zp(s) = 1 Res > I/k. ZP(n)s' Zp(s) is holomorphic for Res > 1/k and it has an analytic continuation in the whole complex s-plane with only possible simple poles at s = j/k (j = 1, 0, -1, -2, -3, . .. ) other than nonpositive integers. In this paper, we shall obtain the explicit value of Zp(-m) for any nonnegative integer m, the asymptotic formula of Zp (s) at s = l/k, the value Z4(0) and its application to the determinants of elliptic operators.