✦ LIBER ✦

Dirichlet series associated with polynomials and applications

✍ Scribed by Yoshio Tanigawa; Wenguang Zhai

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 408 KB
Volume: 122
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.05.004

No coin nor oath required. For personal study only.

✦ Synopsis

We consider the possibility of the analytic continuation of the Dirichlet series S P ;Z (s) associated with a polynomial P (x) and auxiliary series Z(s). In fact, we derive a certain criterion for the analytic continuation for some class of polynomials and give examples such that S P ;Z (s) cannot be continued meromorphically to the whole plane C. We also study the asymptotic behaviors of the sum M P (x) = P (n 1 ,...,n k ) x Λ(n 1 ) • • • Λ(n k ) considered first by M. Peter. Generalizations of this sum are also considered.

📜 SIMILAR VOLUMES

Matrices which generate families of poly

Matrices which generate families of polynomials and associated infinite series

✍ P.R Vein 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 305 KB

Hilbert Spaces of Holomorphic Dirichlet

Hilbert Spaces of Holomorphic Dirichlet Series and Applications to Convolution Equations

✍ Lê Hai Khôi 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 179 KB

We consider Hilbert spaces of holomorphic Dirichlet series in bounded convex domains of C n and apply the results obtained to convolution equations to get the estimates between right-hand sides and particular solutions of such equations.

Hilbert series of quadratic algebras ass

Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials

✍ Israel Gelfand; Sergei Gelfand; Vladimir Retakh; Shirlei Serconek; Robert Lee Wi 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 165 KB

The quadratic algebras Q n are associated with pseudo-roots of noncommutative polynomials. We compute the Hilbert series of the algebras Q n and of the dual algebras Q ! n .

On orthogonal polynomials with positive

On orthogonal polynomials with positive zeros and the associated kernel polynomials

✍ Erik A van Doorn 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 454 KB

One and multidimensional sampling theore

One and multidimensional sampling theorems associated with Dirichlet problems

✍ Mahmoud H. Annaby 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 249 KB

We use the eigenfunction expansion of Green's function of Dirichlet problems to obtain sampling theorems. The analytic properties of the sampled integral transforms as well as the uniform convergence of the sampling series are proved without any restrictions on the integral transforms. We obtain a o

Information measures of Dirichlet distri

Information measures of Dirichlet distribution with applications

✍ Nader Ebrahimi; Ehsan S. Soofi; Shaoqiong (Annie) Zhao 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 475 KB 👁 1 views

## Abstract We explore properties of information measures of the Dirichlet family and related distributions. Representations of the information measures of the Dirichlet family in terms of the information measures of the gamma family reflect the characterization of Dirichlet distribution in terms o