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Value-distribution of zeta-functions

Part of the Lecture Notes in Mathematics book series (LNM,volume 1434)

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References

  1. Bohr, H., Zur Theorie der Riemann’schen Zetafunktion im kritischen Streifen, Acta Math., 40 (1915), 67–100.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bohr, H. und Jessen, B., Über die Wertverteilung der Riemannschen Zetafunktion, Erste Mitteilung, ibid.,, 54 (1930), 1–35; Zweite Mitteilung, ibid., 58 (1932), 1–55.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Borchsenius, V. and Jessen, B., Mean motions and values of the Riemann zeta function, ibid.,, 80 (1948), 97–166.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Chandrasekharan, K. and Narasimhan, R., The approximate functional equation for a class of zeta-functions, Math. Ann., 152 (1963), 30–64.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Good, A., Ein Mittelwertsatz für Dirichletreihen, die Modulformen assoziiert sind, Comment. Math. Helv., 49 (1974), 35–47.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Jessen, B. and Wintner, A., Distribution functions and the Riemann zeta function, Trans. Amer. Math. Soc., 38 (1935), 48–88.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Joyner, D., “Distribution theorems of L-functions,” Longman Scientific & Technical, 1986.

    Google Scholar 

  8. Matsumoto, K., Discrepancy estimates for the value-distribution of the Riemann zeta-function I, Acta Arith., 48 (1987), 167–190; II, in “Number Theory and Combinatorics, Japan 1984”, ed. by J. Akiyama et al., World Scientific, 1985, pp.265–278; III, Acta Arith., 50 (1988), 315–337.

    MathSciNet  MATH  Google Scholar 

  9. —, A probabilistic study on the value-distribution of Dirichlet series attached to certain cusp forms, Nagoya Math. J., 116(1989), to appear.

    Google Scholar 

  10. —, Asymptotic probability measures of zeta-functions of algebraic number fields, preprint.

    Google Scholar 

  11. Potter, H.S.A., The mean values of certain Dirichlet series I, Proc. London Math. Soc., 46 (1940), 467–478.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Prokhorov, Yu.V., Convergence of random processes and limit theorems in probability theory, Teor. Veroyatnost. i Primenen., 1 (1956), 177–238, =Theory of Probab. Appl., 1 (1956), 157–214.

    MathSciNet  MATH  Google Scholar 

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© 1990 Springer-Verlag

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Matsumoto, K. (1990). Value-distribution of zeta-functions. In: Nagasaka, K., Fouvry, E. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 1434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097134

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  • DOI: https://doi.org/10.1007/BFb0097134

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