Uniform bound for Hecke L-functions
Copyright policy )Uniform bound for Hecke L-functions
Our principal aim in the present article is to establish a uniform hybrid bound for individual values on the critical line of Hecke $L$-functions associated with cusp forms over the full modular group. This is rendered in the statement that for $t\ge0$ $$ \eqalignno{H_j(\txt{1\over2}+it)&\ll(��_j+t)^{1/3+��},& (1.1)\cr H_{j,k}(\txt{1\over2}+it)&\ll (k+t)^{1/3+��},&(1.2)\cr} $$ with the common notation to be made precise in the course of discussion. Talks on this and relevant results were delivered by the authors at MF Oberwolfach on September 20, 2004, and at General Assembry of Math. Soc. Japan on March 30, 2005.
50 pages
- University of Tokyo Japan
- TURUN YLIOPISTO Finland
- Nihon University Japan
- University of Turku Finland
- University of Turku Finland
11F66 (Primary), Mathematics - Number Theory, Hecke series, Maass wave forms, 11F66 (Primary); 11M41 (Secondary), Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, spectral theory, 11M41 (Secondary), Langlands \(L\)-functions; one variable Dirichlet series and functional equations, \(\zeta (s)\) and \(L(s, \chi)\), subconvexity bound, FOS: Mathematics, Number Theory (math.NT), Other Dirichlet series and zeta functions
11F66 (Primary), Mathematics - Number Theory, Hecke series, Maass wave forms, 11F66 (Primary); 11M41 (Secondary), Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, spectral theory, 11M41 (Secondary), Langlands \(L\)-functions; one variable Dirichlet series and functional equations, \(\zeta (s)\) and \(L(s, \chi)\), subconvexity bound, FOS: Mathematics, Number Theory (math.NT), Other Dirichlet series and zeta functions
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