JournalsprimsVol. 47, No. 1pp. 257–305

On Certain Arithmetic Functions <i>M</i> (<i>s</i>; <i>z</i><sub>1</sub>; <i>z</i><sub>2</sub>) Associated with Global Fields: Analytic Properties

  • Yasutaka Ihara

    Kyoto University, Japan
On Certain Arithmetic Functions <i>M</i> (<i>s</i>; <i>z</i><sub>1</sub>; <i>z</i><sub>2</sub>) Associated with Global Fields: Analytic Properties cover
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Abstract

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.

Cite this article

Yasutaka Ihara, On Certain Arithmetic Functions <i>M</i> (<i>s</i>; <i>z</i><sub>1</sub>; <i>z</i><sub>2</sub>) Associated with Global Fields: Analytic Properties. Publ. Res. Inst. Math. Sci. 47 (2011), no. 1, pp. 257–305

DOI 10.2977/PRIMS/36