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

Tetsuya Hattori; Kohji Matsumoto

Acta Arithmetica (1995)

- Volume: 71, Issue: 1, page 79-94
- ISSN: 0065-1036

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topTetsuya Hattori, and Kohji Matsumoto. "Large deviations of Montgomery type and its application to the theory of zeta-functions." Acta Arithmetica 71.1 (1995): 79-94. <http://eudml.org/doc/206762>.

@article{TetsuyaHattori1995,

author = {Tetsuya Hattori, Kohji Matsumoto},

journal = {Acta Arithmetica},

keywords = {large deviations; zeta-functions attached to cusp forms; asymptotic probability measures},

language = {eng},

number = {1},

pages = {79-94},

title = {Large deviations of Montgomery type and its application to the theory of zeta-functions},

url = {http://eudml.org/doc/206762},

volume = {71},

year = {1995},

}

TY - JOUR

AU - Tetsuya Hattori

AU - Kohji Matsumoto

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

JO - Acta Arithmetica

PY - 1995

VL - 71

IS - 1

SP - 79

EP - 94

LA - eng

KW - large deviations; zeta-functions attached to cusp forms; asymptotic probability measures

UR - http://eudml.org/doc/206762

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] 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.) Zbl40.0232.08
- [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. Zbl0675.10017
- [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. Zbl0715.11043
- [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. Zbl0797.11068
- [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. Zbl0641.60032
- [10] M. Ram Murty, Oscillations of Fourier coefficients of modular forms, Math. Ann. 262 (1983), 431-446. Zbl0489.10020
- [11] R. A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985), 593-600. Zbl0556.10018
- [12] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, 1927. Zbl45.0433.02

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