Geodesic
On Non-Vanishing of Convolution of Dirichlet Series
Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 321-332

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

We study the non-vanishing on the line $\operatorname{Re}\left( s \right)=1$ of the convolution series associated to two Dirichlet series in a certain class of Dirichlet series. The non-vanishing of various $L$ -functions on the line $\operatorname{Re}\left( s \right)=1$ will be simple corollaries of our general theorems.
DOI : 10.4153/CMB-2005-030-6
Mots-clés : 11M41 
Akbary, Amir; Shahabi, Shahab. On Non-Vanishing of Convolution of Dirichlet Series. Canadian mathematical bulletin, Tome 48 (2005) no. 3, pp. 321-332. doi: 10.4153/CMB-2005-030-6
@article{10_4153_CMB_2005_030_6,
     author = {Akbary, Amir and Shahabi, Shahab},
     title = {On {Non-Vanishing} of {Convolution} of {Dirichlet} {Series}},
     journal = {Canadian mathematical bulletin},
     pages = {321--332},
     year = {2005},
     volume = {48},
     number = {3},
     doi = {10.4153/CMB-2005-030-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-030-6/}
}
TY  - JOUR
AU  - Akbary, Amir
AU  - Shahabi, Shahab
TI  - On Non-Vanishing of Convolution of Dirichlet Series
JO  - Canadian mathematical bulletin
PY  - 2005
SP  - 321
EP  - 332
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-030-6/
DO  - 10.4153/CMB-2005-030-6
ID  - 10_4153_CMB_2005_030_6
ER  - 
%0 Journal Article
%A Akbary, Amir
%A Shahabi, Shahab
%T On Non-Vanishing of Convolution of Dirichlet Series
%J Canadian mathematical bulletin
%D 2005
%P 321-332
%V 48
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-030-6/
%R 10.4153/CMB-2005-030-6
%F 10_4153_CMB_2005_030_6

[1] [1] Davenport, H., Multiplicative Number Theory. Third ed. Graduate Texts in Mathematics 74, Springer-Verlag, New York, 2000. Google Scholar

[2] [2] Ingham, A. E., Note on Riemann's ζ-function and Dirichlet's L-functions. J. London Math. Soc. 5(1930), 107–112. Google Scholar

[3] [3] Jacquet, H. and Shalika, J. A., A non-vanishing theorem for zeta functions of GL , Inventiones Math. 38(1976), 1–16. Google Scholar

[4] [4] Koblitz, N., Introduction to elliptic curves and modular forms. Second ed. Springer-Verlag, New York, 1993. Google Scholar

[5] [5] Murty, M. R., Problems in Analytic Number Theory. Graduate Texts in Mathematics 206, Springer-Verlag, New York, 2001. Google Scholar

[6] [6] Murty, V. K., On the Sato-Tate conjecture. Prog. Math. 26(1982), 195–205. Google Scholar

[7] [7] Narayanan, S., On the non-vanishing of a certain class of Dirichlet series. Canad. Math. Bull. 40(1997), 364–369. Google Scholar

[8] [8] Ogg, A. P., On a convolution of L-series. Invent. Math. 7(1969), 297–312. Google Scholar

[9] [9] Rankin, R. A., Contributions to the theory of Ramanujan's function τ (n) and similar arithmetical functions. I. Proc. Camb. Phil. Soc. 35(1939), 351–356. Google Scholar

[10] [10] Rankin, R. A., Contributions to the theory of Ramanujan's function τ (n) and similar arithmetical functions. II. Proc. Camb. Phil. Soc. 35(1939), 357–372. Google Scholar

[11] [11] Shahidi, F., On non-vanishing of L-functions, Bull. Amer.Math. Soc. (N.S.) 2(1980), 462–464. Google Scholar

[12] [12] Shahidi, F., On non-vanishing of twisted symmetric and exterior square L-functions for GL(n), Pacific J. Math. 181(1997), 311–322. Google Scholar

Cité par Sources :