منابع مشابه
Note on Absolutely Convergent Dirichlet Series
is it true that \f(s)\ s^k>0 for cr^O implies that (/(s))-1 is also of the form (1)? In this note, an affirmative answer is supplied.3 Let P be the semigroup of positive integers under multiplication, and let h(P) be the class of all complex functions a on P, a= {an}»~i, for which ||a|| = y^°-i \an\ is finite. We obtain a commutative Banach algebra by defining (aa)n = aan for complex a, (a+b)n ...
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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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Denoting by r(k, m, p) the first occurrence of m consecutive fcth power residues of a prime p = 1 (mod k), we show that r(k, m, p) > c log p for infinitely many p (c is an absolute constant) provided that k is even and m ä 3.
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The set of the generalized factorials {(x|d)i}i=0 is a basis of the vector space of all real polynomials of degree at most n, where (x|d)i = x(x − d) · · · (x − id + d) and d is a fixed negative real number. In this note, we show that if a polynomial has only real nonpositive zeros in the standard basis, then so does the polynomial having the same coefficients with the former in the basis {(x|d...
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satisfying zZ\ \^A < °°, if and only if f is) is bounded away from zero in the half-plane 0-3:0. This discovery amounts to a determination of the spectrum of the Banach-algebra element associated with fis), and it thus makes available for the theory of ordinary Dirichlet series the well-known theorem of Gelfand on analytic functions of Banach-algebra elements (see §24D of [7]) and its generaliz...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1922
ISSN: 0002-9947
DOI: 10.2307/1988909