Publications of the Research Institute for Mathematical Sciences


Full-Text PDF (485 KB) | Metadata | Table of Contents | PRIMS summary
Volume 47, Issue 1, 2011, pp. 257–305
DOI: 10.2977/PRIMS/36

Published online: 2011-03-24

On Certain Arithmetic Functions M (s; z1; z2) Associated with Global Fields: Analytic Properties

Yasutaka Ihara[1]

(1) Kyoto University, Japan

The arithmetic functions in the title arose from value-distribution theories related to L-functions of global elds. They are "complexi cations" 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