Geodesic
Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
Acta Arithmetica, Tome 84 (1998) no. 2, pp. 155-192

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 be removed from the final result. Similar results are obtained for the tails of Dirichlet series. Four examples of applications to the Riemann zeta-function are included.
DOI : 10.4064/aa-84-2-155-192

D. Goldston 1 ; S. Gonek 1

1 
@article{10_4064_aa_84_2_155_192,
     author = {D. Goldston and S. Gonek},
     title = {Mean value theorems for long {Dirichlet} polynomials and tails of {Dirichlet} series},
     journal = {Acta Arithmetica},
     pages = {155--192},
     publisher = {mathdoc},
     volume = {84},
     number = {2},
     year = {1998},
     doi = {10.4064/aa-84-2-155-192},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa-84-2-155-192/}
}
TY  - JOUR
AU  - D. Goldston
AU  - S. Gonek
TI  - Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
JO  - Acta Arithmetica
PY  - 1998
SP  - 155
EP  - 192
VL  - 84
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa-84-2-155-192/
DO  - 10.4064/aa-84-2-155-192
LA  - en
ID  - 10_4064_aa_84_2_155_192
ER  - 
%0 Journal Article
%A D. Goldston
%A S. Gonek
%T Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series
%J Acta Arithmetica
%D 1998
%P 155-192
%V 84
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa-84-2-155-192/
%R 10.4064/aa-84-2-155-192
%G en
%F 10_4064_aa_84_2_155_192
D. Goldston; S. Gonek. Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series. Acta Arithmetica, Tome 84 (1998) no. 2, pp. 155-192. doi: 10.4064/aa-84-2-155-192

Cité par Sources :