Publications of the Research Institute for Mathematical Sciences
Full-Text PDF (485 KB) | Metadata | Table of Contents | PRIMS summary
Published online: 2011-03-24
On Certain Arithmetic Functions M (s; z1; z2) Associated with Global Fields: Analytic PropertiesYasutaka Ihara (1) Kyoto University, Japan
The arithmetic functions in the title arose from value-distribution theories related to L-functions of global elds. They are "complexications" of the Fourier duals of the corresponding density functions. We shall study their complex analytic properties including analytic continuations and the limit behaviors at the critical point s = 1/2.
Keywords: L-function, arithmetic function, critical point, Plancherel equality, probabilistic inequality.
Ihara Yasutaka: On Certain Arithmetic Functions M (s; z1; z2) Associated with Global Fields: Analytic Properties. Publ. Res. Inst. Math. Sci. 47 (2011), 257-305. doi: 10.2977/PRIMS/36