Value-distribution of zeta-functions

Matsumoto, Kohji

doi:10.1007/bfb0097134

Cited by 76 publications

(85 citation statements)

References 9 publications

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“…On p.179 of [11], it is mentioned that the Euler product (1) is convergent absolutely, under the condition (2), in the region σ > α + β + 1. This can be seen by the estimate…”

Section: Appendixmentioning

confidence: 99%

Remarks on the Mixed Joint Universality for A class of Zeta Functions

Kačinskaitė

Matsumoto²

2016

Bull. Aust. Math. Soc.

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“…On p.179 of [11], it is mentioned that the Euler product (1) is convergent absolutely, under the condition (2), in the region σ > α + β + 1. This can be seen by the estimate…”

Section: Appendixmentioning

confidence: 99%

Remarks on the Mixed Joint Universality for A class of Zeta Functions

Kačinskaitė

Matsumoto²

2016

Bull. Aust. Math. Soc.

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“…was proved in Matsumoto [11] or [13], and Joyner's type inequality for W (C \ R( ), σ, ζ F ) was given in Matsumoto [12]. In this section, as a generalization of Theorem 1, we prove the following theorem, which implies that the asymptotic behavior of W (C \ R( ), σ, ζ F ) is ruled only by σ and the degree d. …”

Section: Dedekind Zeta-functions Of Galois Number Fieldsmentioning

confidence: 73%

A limit theorem for Bohr-Jessen's probability measures of the Riemann zeta-function

Matsumoto¹,

Hattori²

1999

Journal f�r die reine und angewandte Mathematik (Crelles Journ

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The asymptotic behavior of value distribution of the Riemann zeta-function ζ(s) is determined for 1 2 < (s) < 1. Namely, the existence is proved, and the value is given, of the limitfor 1 2 < σ < 1, where R( ) is a square in the complex plane C of side length 2 centered at 0, andwhere µ 1 is the one-dimensional Lebesgue measure. Analogous results are obtained also for the Dedekind zeta-functions of Galois number fields. As an essential step, a limit theorem for a sum of independent random vari-r n X n is proved, where X n , n ∈ N, have identical distribution on a finite interval with mean zero, and {r n } is a regularly varying sequence of index −σ. The limit theorem states the convergence ofand gives the explicit value of the limit. In particular, it is shown that the value depends only on σ and is otherwise independent of {r n }.0 1991 Mathematics Subject Classification. 11M06, 60G50

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“…Meanwhile, it is known that there exists a rich zoo of universal Dirichlet series; for a list we refer to [Lau96], [Mat04], [Ste04]. It was conjectured by Linnik and Ibragimov that all functions given by Dirichlet series and analytically continuable to the left of the half plane of absolute convergence, which satisfy some natural growth conditions, are universal.…”

Section: The Selberg Classmentioning

confidence: 99%

Mathematisches Institut Georg-August-Universität Göttingen Seminars Winter Term 2004/2005

Tschinkel¹

2005

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Value-distribution of zeta-functions

Cited by 76 publications

References 9 publications

Remarks on the Mixed Joint Universality for A class of Zeta Functions

Remarks on the Mixed Joint Universality for A class of Zeta Functions

A limit theorem for Bohr-Jessen's probability measures of the Riemann zeta-function

Mathematisches Institut Georg-August-Universität Göttingen Seminars Winter Term 2004/2005

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