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ArticleOriginal scientific text

Title

Large deviations of Montgomery type and its application to the theory of zeta-functions

Authors 1, 2

Affiliations

  1. Department of Information Sciences, Faculty of Engineering, Utsunomiya University, Ishii-Cho, Utsunomiya 321, Japan
  2. 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. D. Joyner, Distribution Theorems of L-functions, Longman Scientific & Technical, 1986.
  3. E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Erster Band, Teubner, 1909. (Third ed., Chelsea, 1974.)
  4. K. Matsumoto, A probabilistic study on the value-distribution of Dirichlet series attached to certain cusp forms, Nagoya Math. J. 116 (1989), 123-138.
  5. 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.
  6. K. Matsumoto, On the magnitude of asymptotic probability measures of Dedekind zeta-functions and other Euler products, Acta Arith. 60 (1991), 125-147.
  7. K. Matsumoto, Asymptotic probability measures of Euler products, in: Proceedings of the Amalfi Conference on Analytic Number Theory, E. Bombieri et al. (eds.), Univ. di Salerno, 1992, 295-313.
  8. 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
  9. H. L. Montgomery and A. M. Odlyzko, Large deviations of sums of independent random variables, Acta Arith. 49 (1988), 427-434.
  10. M. Ram Murty, Oscillations of Fourier coefficients of modular forms, Math. Ann. 262 (1983), 431-446.
  11. R. A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985), 593-600.
  12. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, 1927.
Acta Arithmetica
1995/71/1
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Pages:
79-94
Main language of publication
English
Received
1994-04-13
Accepted
1994-07-26
Published
1995
Exact and natural sciences