منابع مشابه
Dirichlet Series
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...
متن کاملDirichlet Series
where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...
متن کاملDirichlet series and hyperelliptic curves
For a fixed hyperelliptic curve C given by the equation y 1⁄4 f ðxÞ with f A Z1⁄2x having distinct roots and degree at least 5, we study the variation of rational points on the quadratic twists Cm whose equation is given by my 2 1⁄4 f ðxÞ. More precisely, we study the Dirichlet series Df ðsÞ 1⁄4 P 0 m00aCmðQÞjmj s where the summation is over all non-zero squarefree integers. We show that Df ðsÞ...
متن کاملOn Kubota’s Dirichlet Series
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...
متن کاملMultiple Dirichlet Series
This introductory article aims to provide a roadmap to many of the interrelated papers in this volume and to a portion of the field of multiple Dirichlet series, particularly emerging new ideas. It is both a survey of the recent literature, and an introduction to the combinatorial aspects of Weyl group multiple Dirichlet series, a class of multiple Dirichlet series that are not Euler products, ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1985
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500006066