Geodesic
LOCAL SUPREMA OF DIRICHLET POLYNOMIALS AND ZEROFREE REGIONS OF THE RIEMANN ZETA-FUNCTION
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 643-655

Voir la notice de l'article provenant de la source Cambridge

DOI

A new family of zerofree region of the Riemann Zeta-function ζ is identified by using Turán's (P. Turán, Eine neue Methode inter Analysis und deren Anwendungen (Akadémiai Kiadó, Budapest, Hungary, 1953); Analytic number theory, Proc. Symp. Pure Math., vol. XXIV (Amer. Math. Soc. Providence, RI, 1972)) localization criterion linking zeros of ζ with uniform local suprema of sets of Dirichlet polynomials expanded over the primes. The proof is based on a randomization argument. An estimate for local extrema for some finite families of shifted Dirichlet polynomials is established by preliminary considering their local increment properties by means of Montgomery-Vaughan's variant of Hilbert's inequality. A covering argument combined with Turán's localization criterion allows to conclude.
DOI : 10.1017/S001708951400007X
Mots-clés : Primary: 11M26, Secondary: 26D05, 60G17 
WEBER, MICHEL J. G. LOCAL SUPREMA OF DIRICHLET POLYNOMIALS AND ZEROFREE REGIONS OF THE RIEMANN ZETA-FUNCTION. Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 643-655. doi: 10.1017/S001708951400007X
@article{10_1017_S001708951400007X,
     author = {WEBER, MICHEL J. G.},
     title = {LOCAL {SUPREMA} {OF} {DIRICHLET} {POLYNOMIALS} {AND} {ZEROFREE} {REGIONS} {OF} {THE} {RIEMANN} {ZETA-FUNCTION}},
     journal = {Glasgow mathematical journal},
     pages = {643--655},
     year = {2014},
     volume = {56},
     number = {3},
     doi = {10.1017/S001708951400007X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951400007X/}
}
TY  - JOUR
AU  - WEBER, MICHEL J. G.
TI  - LOCAL SUPREMA OF DIRICHLET POLYNOMIALS AND ZEROFREE REGIONS OF THE RIEMANN ZETA-FUNCTION
JO  - Glasgow mathematical journal
PY  - 2014
SP  - 643
EP  - 655
VL  - 56
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S001708951400007X/
DO  - 10.1017/S001708951400007X
ID  - 10_1017_S001708951400007X
ER  - 
%0 Journal Article
%A WEBER, MICHEL J. G.
%T LOCAL SUPREMA OF DIRICHLET POLYNOMIALS AND ZEROFREE REGIONS OF THE RIEMANN ZETA-FUNCTION
%J Glasgow mathematical journal
%D 2014
%P 643-655
%V 56
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S001708951400007X/
%R 10.1017/S001708951400007X
%F 10_1017_S001708951400007X

Cité par Sources :