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

• Autorzy: Kohji Matsumoto
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1991-1992
• Tom: 60
• Numer: 2
• Strony: 125-147

Daty

wydano

1991

otrzymano

1990-08-02

poprawiono

1990-12-04

Twórcy

autor

Kohji Matsumoto

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

Bibliografia

• [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