2021-12-03T11:23:55Zhttps://nagoya.repo.nii.ac.jp/oaioai:nagoya.repo.nii.ac.jp:000179802021-03-01T16:51:48ZOn log L and L'/L for L-Functions and the Associated “M-Functions”: Connections in Optimal CasesIHARA, YASUTAKA52457MATSUMOTO, KOHJI52458Let L(s,χ) be either log L(s,χ) or L'/L(s,χ), associated with an (abelian) L-function L(s,χ) of a global field K. For any quasi-character ψ: ℂ→ℂ× of the additive group of complex numbers, consider the average “Avgfχ=f” of ψ(L(s,χ)) over all Dirichlet characters χ on K with a given prime conductor f. This paper contains (i) study of the limit as N(f)→∞ of this average, (ii) basic studies of the analytic function Ms(z1,z2) in 3 complex variables arising from (i) (here, (z1,z2)∈ℂ2 is the natural parameter for ψ), and (iii) application to value-distribution theory for {L(s,χ)}χ. Our base field K is either a function field over a finite field, or a special type of number field: the rational number field ℚ or an imaginary quadratic field. But in the number field case, the Generalized Riemann Hypothesis is assumed in (i) and (iii).journal articleIndependent University of Moscow2011application/pdfMOSCOW MATHEMATICAL JOURNAL11173111http://hdl.handle.net/2237/200721609-4514https://nagoya.repo.nii.ac.jp/record/17980/files/13.pdfeng