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

How to cite

top

Tetsuya 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. [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. [2] D. Joyner, Distribution Theorems of L-functions, Longman Scientific & Technical, 1986. 
  3. [3] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Erster Band, Teubner, 1909. (Third ed., Chelsea, 1974.) Zbl40.0232.08
  4. [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. [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. [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. [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. [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. [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. [10] M. Ram Murty, Oscillations of Fourier coefficients of modular forms, Math. Ann. 262 (1983), 431-446. Zbl0489.10020
  11. [11] R. A. Rankin, Sums of powers of cusp form coefficients II, Math. Ann. 272 (1985), 593-600. Zbl0556.10018
  12. [12] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed., Cambridge Univ. Press, 1927. Zbl45.0433.02

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.