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The order of certain Dirichlet series
Published online by Cambridge University Press: 09 April 2009
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This paper is a continuation of [1]1 We shall use the same notations as those in [1]. Let F(X) ∈ R[X], X = (X1, …, Xn), be a polynomial of degree d > 0 and h(x) ∈ SP(Rn), i.e. h(x) is the sum of a polynomial and a Schwartz funtion. We shall consider Dirichlet series of the type 
where NF = {x∈Rn: F(x) = 0}. We proved, in [1], that Z(h, F, s) is regular for σ > (n+p)/d and possesses the analytic continuation to the whole s-plane when Fd(x) (the highest homogeneous part of F(X)) ≠ 0 for x ≠ 0. In this paper, we shall say the following.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 12 , Issue 4 , November 1971 , pp. 441 - 443
- Copyright
- Copyright © Australian Mathematical Society 1971
References
[1]An, Chung-ming, On a generalization of Gamma function and its application to certain D richlet series (Dissertation, University of Pennsylvania, 1969).CrossRefGoogle Scholar
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