On “-Functions” Closely Related to the Distribution of -Values

  • Yasutaka Ihara

    Kyoto University, Japan

Abstract

For each global field , we shall construct and study two basic arithmetic functions, and its Fourier dual , on parametrized by . These functions are closely related to the density measure for the distribution of values on of the logarithmic derivatives of -functions , where is fixed, with , and runs over a natural infinite family of Dirichlet or Hecke characters on . Connections with the Bohr–Jessen type value-distribution theories for the logarithms or (not much studied) logarithmic derivatives of , where is fixed and varies, will also be briefly discussed.

Cite this article

Yasutaka Ihara, On “-Functions” Closely Related to the Distribution of -Values. Publ. Res. Inst. Math. Sci. 44 (2008), no. 3, pp. 893–954

DOI 10.2977/PRIMS/1216238306