Dirichlet series associated with polynomials
نویسندگان
چکیده
منابع مشابه
Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications b...
متن کاملDirichlet Series Associated to Quartic Fields with given Resolvent
Let k be a cubic field. We give an explicit formula for the Dirichlet series P K |Disc(K)| −s, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to k. Our work is a sequel to the unpublished preprint [11] whose results have been summarized in [6], so we include complete proofs so as not to rely on unpublished work. This is a companion pape...
متن کاملDirichlet series associated to quartic fields with given cubic resolvent
Let k be a cubic field. We give an explicit formula for the Dirichlet series ∑ K |Disc(K)|−s, where the sum is over isomorphism classes of all quartic fields whose cubic resolvent field is isomorphic to k. Our work is a sequel to the unpublished preprint [12] whose results have been summarized in [7], so we include complete proofs so as not to rely on unpublished work. This is a companion paper...
متن کاملDirichlet orthogonal polynomials with Laguerre weight
Let {λj}j=1 be a sequence of distinct positive numbers. We find explicit formulae for the orthogonal Dirichlet polynomials {ψn} formed from linear combinations of { λ−it j }n j=1 , associated with the Laguerre weight. Thus ∫ ∞ 0 ψn (t)ψm (t)e −tdt = δmn. In addition, we estimate Christoffel functions and establish Markov-Bernstein inequalities.
متن کاملOrthogonal Dirichlet polynomials with arctangent density
Let {λj}∞j=1 be a strictly increasing sequence of positive numbers with λ1 = 1. We find a simple explicit formula for the orthogonal Dirchlet polynomials {φn} formed from linear combinations of { λ j n j=1 , associated with the arctangent density. Thus ∫ ∞ −∞ φn (t)φm (t) dt π (1 + t2) = δmn. We obtain formulae for their Christoffel functions, and deduce their asymptotics, as well as universali...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1998
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-84-3-245-278