The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to ...The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.展开更多
Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust ...Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.展开更多
A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（g...A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.展开更多
基金Acknowledgements The authors would like to show their hearty thanks to Professor Shigeru Kanemitsu for enlightening discussion and encouragement. The second author was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101175, 11371165）, 985 Project, and 211 Project.
文摘The aim of this paper is two folds. First, we shall prove a general reduction theorem to the Spannenintegral of products of （generalized） Kubert functions. Second, we apply the special case of Carlitz＇s theorem to the elaboration of earlier results on the mean values of the product of Dirichlet L-functions at integer arguments. Carlitz＇s theorem is a generalization of a classical result of Nielsen in 1923. Regarding the reduction theorem, we shall unify both the results of Carlitz （for sums） and Mordell （for integrals）, both of which are generalizations of preceding results by Frasnel, Landau, Mikolas, and Romanoff et al. These not only generalize earlier results but also cover some recent results. For example, Beck＇s lamma is the same as Carlitz＇s result, while some results of Maier may be deduced from those of Romanoff. To this end, we shall consider the Stiletjes integral which incorporates both sums and integrals. Now, we have an expansion of the sum of products of Bernoulli polynomials that we may apply it to elaborate on the results of afore-mentioned papers and can supplement them by related results.
文摘Using series iteration techniques identities and apply each of these identities in we derive a number of general double series order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.
基金Supported by the National Natural Science Foundation of China (Grant No.10671142)
文摘A monomial basis and a filtration of subalgebras for the universal enveloping algebra U（gl） of a complex simple Lie algebra gl of type Bl and Cl are given, and the decomposition of the Weyl module V （λ） as a U（gl）-module into a direct sum of Weyl modules V （μ）’s as U（gl-1）modules is described. In particular, a new multiplicity formula for the Weyl module V （λ） is obtained in this note.
