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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The paper reviews some of the early ideas behind the development of the theory of discrete harmonic functions. The connection to random walks is pointed out. Then a current and more general construction using weight functions is described. Discrete analogues of the Laplace operator are defined for Zn and a discrete planar hexagonal structure H. Discrete analogues of the Dirichlet problem and Po...
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This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1968
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708950000032x