m at h . N T ] 1 4 M ay 2 00 9 CONSTRUCTING WEYL GROUP MULTIPLE DIRICHLET SERIES
نویسنده
چکیده
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for Re(si) sufficiently large, that has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. A heuristic definition of such series was given in [BBC06], and they have been investigated in certain special cases in [BBC06,BBF06,BBFH07, BBF08, BBFa, CG07, CFG08, CG, Chi05]. In this paper we generalize results in [CG] to construct Weyl group multiple Dirichlet series by a uniform method, and show in all cases that they have the expected properties.
منابع مشابه
ec 2 00 6 ON THE p - PARTS OF QUADRATIC WEYL GROUP MULTIPLE DIRICHLET SERIES
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large, which has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. Two constructions of such series are available, one [1...
متن کامل2 00 6 ON THE p - PARTS OF QUADRATIC WEYL GROUP MULTIPLE DIRICHLET SERIES
Let Φ be a reduced root system of rank r. A Weyl group multiple Dirichlet series for Φ is a Dirichlet series in r complex variables s1, . . . , sr, initially converging for R(si) sufficiently large, which has meromorphic continuation to C and satisfies functional equations under the transformations of C corresponding to the Weyl group of Φ. Two constructions of such series are available, one [1...
متن کاملar X iv : h ep - t h / 99 05 04 6 v 2 1 0 M ay 1 99 9 Counterterms for the Dirichlet Prescription of the AdS / CFT Correspondence
We illustrate the Dirichlet prescription of the AdS/CFT correspondence using the example of a massive scalar field and argue that it is the only entirely consistent regularization procedure known so far. Using the Dirichlet prescription, we then calculate the divergent terms for gravity in the cases d = 2, 4, 6, which give rise to the Weyl anomaly in the boundary conformal field theory. E-mail:...
متن کاملConstructing Weyl Group Multiple Dirichlet Series
This paper describes a technique to construct Weyl group multiple Dirichlet series. Such series were first introduced in [BBC06], which also described a heuristic means to define, analytically continue, and prove functional equations for a family of Dirichlet series in several complex variables. Several subsequent papers have dealt with the problem of making the heuristic definitions precise an...
متن کاملar X iv : h ep - t h / 99 05 04 6 v 1 6 M ay 1 99 9 Counterterms for the Dirichlet Prescription of the AdS / CFT Correspondence
We illustrate the Dirichlet prescription of the AdS/CFT correspondence using the example of a massive scalar field and argue that it is the only entirely consistent regularization procedure known so far. Using the Dirichlet prescription, we then calculate the divergent terms for gravity in the cases d = 2, 4, 6, which give rise to the Weyl anomaly in the boundary conformal field theory. E-mail:...
متن کامل