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

Acta Arithmetica (1991)

- Volume: 60, Issue: 2, page 125-147
- ISSN: 0065-1036

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topKohji Matsumoto. "On the magnitude of asymptotic probability measures of Dedekind zeta-functions and other Euler products." Acta Arithmetica 60.2 (1991): 125-147. <http://eudml.org/doc/206429>.

@article{KohjiMatsumoto1991,

author = {Kohji Matsumoto},

journal = {Acta Arithmetica},

keywords = {Montgomery's inequality; sums of independent random variables; Dedekind zeta-functions; zeta-functions associated with certain cusp forms},

language = {eng},

number = {2},

pages = {125-147},

title = {On the magnitude of asymptotic probability measures of Dedekind zeta-functions and other Euler products},

url = {http://eudml.org/doc/206429},

volume = {60},

year = {1991},

}

TY - JOUR

AU - Kohji Matsumoto

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

JO - Acta Arithmetica

PY - 1991

VL - 60

IS - 2

SP - 125

EP - 147

LA - eng

KW - Montgomery's inequality; sums of independent random variables; Dedekind zeta-functions; zeta-functions associated with certain cusp forms

UR - http://eudml.org/doc/206429

ER -

## References

top- [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. Zbl56.0287.01
- [2] K. Chandrasekharan and R. Narasimhan, The approximate functional equation for a class of zeta-functions, Math. Ann. 152 (1963), 30-64. Zbl0116.27001
- [3] T. Hattori and K. Matsumoto, Large deviations of Montgomery type and its application to the theory of zeta-functions, preprint. Zbl0818.11032
- [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. Zbl0675.10017
- [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. Zbl0746.11051
- [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. Zbl0641.60032
- [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. Zbl66.0340.01
- [13] R. A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985), 593-600 Zbl0556.10018

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