On certain arithmetical Dirichlet series
نویسندگان
چکیده
منابع مشابه
The Critical Values of Certain Dirichlet Series
We investigate the values of several types of Dirichlet series D(s) for certain integer values of s, and give explicit formulas for the value D(s) in many cases. The easiest types of D are Dirichlet L-functions and their variations; a somewhat more complex case involves elliptic functions. There is one new type that includes ∑∞ n=1(n +1) for which such values have not been studied previously. 2...
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by giving a representation of L(s) in terms of Hurwitz zeta functions. That representation allowed us to get some information about zeros and poles; nevertheless no functional equation could be deduced from it. In this paper following a classical argument we obtain for L(s) as above, under suitable hypothesis, a functional equation of Riemann’s type. More precisely, let us consider the Dirichle...
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We consider a certain multiple Dirichlet series which is a generalization of that introduced in Masri, and we prove the meromorphic continuation to the whole space. Also, using certain functional relations and the technique of chaging variables introduced in Akiyama, Egami and Tanigawa, we prove that " the possible singularities " is indeed " the true singularities " .
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Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [2]. Closely related results are in Eckhardt and Pat...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1964
ISSN: 0025-5645
DOI: 10.2969/jmsj/01630214