Geodesic
Nonvanishing of L-functions, the Ramanujan Conjecture, and Families of Hecke Characters
Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 22-51

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DOI

We prove a nonvanishing result for families of $\text{G}{{\text{L}}_{n}}\times \text{G}{{\text{L}}_{n}}$ Rankin–Selberg $L$ -functions in the critical strip, as one factor runs over twists by Hecke characters. As an application, we simplify the proof, due to Luo, Rudnick, and Sarnak, of the best known bounds towards the Generalized Ramanujan Conjecture at the infinite places for cusp forms on $\text{G}{{\text{L}}_{n}}$ . A key ingredient is the regularization of the units in residue classes by the use of an Arakelov ray class group.
DOI : 10.4153/CJM-2011-068-7
Mots-clés : 11F70, 11M41, nonvanishing, automorphic forms, Hecke characters, Ramanujan conjecture 
Blomer, Valentin; Brumley, Farrell. Nonvanishing of L-functions, the Ramanujan Conjecture, and Families of Hecke Characters. Canadian journal of mathematics, Tome 65 (2013) no. 1, pp. 22-51. doi: 10.4153/CJM-2011-068-7
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     title = {Nonvanishing of {L-functions,} the {Ramanujan} {Conjecture,} and {Families} of {Hecke} {Characters}},
     journal = {Canadian journal of mathematics},
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     year = {2013},
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