Geodesic
On the Non-Vanishing of a Certain Class of Dirichlet Series
Canadian mathematical bulletin, Tome 40 (1997) no. 3, pp. 364-369

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In this paper, we consider Dirichlet series with Euler products of the form F(s) = Πp in > 1, and which are regular in ≥ 1 except for a pole of order m at s = 1. We establish criteria for such a Dirichlet series to be nonvanishing on the line of convergence. We also show that our results can be applied to yield non-vanishing results for a subclass of the Selberg class and the Sato-Tate conjecture.
DOI : 10.4153/CMB-1997-043-6
Mots-clés : Primary: 11Mxx, Secondary: 11M41 
Narayanan, Sridhar. On the Non-Vanishing of a Certain Class of Dirichlet Series. Canadian mathematical bulletin, Tome 40 (1997) no. 3, pp. 364-369. doi: 10.4153/CMB-1997-043-6
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     title = {On the {Non-Vanishing} of a {Certain} {Class} of {Dirichlet} {Series}},
     journal = {Canadian mathematical bulletin},
     pages = {364--369},
     year = {1997},
     volume = {40},
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     doi = {10.4153/CMB-1997-043-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-043-6/}
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