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ArticleOriginal scientific text

Title

On the magnitude of asymptotic probability measures of Dedekind zeta-functions and other Euler products

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Education, Iwate University, Ueda, Morioka 020, Japan

Bibliography

  1. H. Bohr und B. Jessen, Über die Wertverteilung der Riemannschen Zetafunktion, Erste Mitteilung, Acta Math. 54 (1930), 1-35; Zweite Mitteilung, Acta Math. 58 (1932), 1-55.
  2. K. Chandrasekharan and R. Narasimhan, The approximate functional equation for a class of zeta-functions, Math. Ann. 152 (1963), 30-64.
  3. T. Hattori and K. Matsumoto, Large deviations of Montgomery type and its application to the theory of zeta-functions, preprint.
  4. B. Jessen and A. Wintner, Distribution functions and the Riemann zeta function, Trans. Amer. Math. Soc. 38 (1935), 48-88.
  5. D. Joyner, Distribution Theorems of L-functions, Longman Scientific & Technical, 1986.
  6. K. Matsumoto, A probabilistic study on the value-distribution of Dirichlet series attached to certain cusp forms, Nagoya Math. J. 116 (1989), 123-138.
  7. K. Matsumoto, Value-distribution of zeta-functions, in: Analytic Number Theory , Proceedings of the Japanese-French Symposium held in Tokyo, Oct. 10-13, 1988, K. Nagasaka and E. Fouvry (eds.), Lecture Notes in Math. 1434, Springer, 1990, 178-187.
  8. K. Matsumoto, Asymptotic probability measures of zeta-functions of algebraic number fields, J. Number Theory, to appear.
  9. H. L. Montgomery, The zeta function and prime numbers, in: Proceedings of the Queen's Number Theory Conference, 1979, P. Ribenboim (ed.), Queen's Papers in Pure and Appl. Math. 54, Queen's Univ., Kingston, Ont., 1980, 1-31.
  10. H. L. Montgomery and A. M. Odlyzko, Large deviations of sums of independent random variables, Acta Arith. 49 (1988), 427-434.
  11. E. M. Nikishin, Dirichlet series with independent exponents and some of their applications, Mat. Sb. 96 (138) (1975), 3-40 = Math. USSR-Sb. 25 (1975), 1-36.
  12. H. S. A. Potter, The mean values of certain Dirichlet series I, Proc. London Math. Soc. 46 (1940), 467-478.
  13. R. A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985), 593-600
Acta Arithmetica
1991-1992/60/2
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Pages:
125-147
Main language of publication
English
Received
1990-08-02
Accepted
1990-12-04
Published
1991
Exact and natural sciences