On zeta-functions associated to certain cusp forms. I

A. Laurinčikas; J. Steuding

Open Mathematics (2004)

  • Volume: 2, Issue: 1, page 1-18
  • ISSN: 2391-5455

Abstract

top
In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained.

How to cite

top

A. Laurinčikas, and J. Steuding. "On zeta-functions associated to certain cusp forms. I." Open Mathematics 2.1 (2004): 1-18. <http://eudml.org/doc/268697>.

@article{A2004,
abstract = {In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained.},
author = {A. Laurinčikas, J. Steuding},
journal = {Open Mathematics},
keywords = {11M41; 11N37},
language = {eng},
number = {1},
pages = {1-18},
title = {On zeta-functions associated to certain cusp forms. I},
url = {http://eudml.org/doc/268697},
volume = {2},
year = {2004},
}

TY - JOUR
AU - A. Laurinčikas
AU - J. Steuding
TI - On zeta-functions associated to certain cusp forms. I
JO - Open Mathematics
PY - 2004
VL - 2
IS - 1
SP - 1
EP - 18
AB - In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained.
LA - eng
KW - 11M41; 11N37
UR - http://eudml.org/doc/268697
ER -

References

top
  1. [1] H. Bohr: “Über Diophantische Approximationen und ihre Anwendung auf Dirichletsche Reihen, besonders auf die Riemannsche Zetafunktion”, In: Proc. 5th Congress of Scand. Math., 1923, Helsingfors, pp. 131–154. 
  2. [2] H. Bohr and B. Jessen: “Über die Wertverteilung der Riemannschen Zetafunktion, Erste Mitteilung”, Acta Math., Vol. 54, (1930), pp. 1–35. Zbl56.0287.01
  3. [3] H. Bohr and B. Jessen: “Über die Wertverteilung der Riemannschen Zetafunktion, Zweite Mitteilung”, Acta Math., Vol. 58, (1932), pp. 1–55. Zbl0003.38901
  4. [4] P. Deligne: “La conjecture de Weil”, Inst. Hautes Etudes Sci. Publ. Math., Vol. 43, (1974), pp. 273–307. Zbl0287.14001
  5. [5] F. Grupp: “Eine Bemerkung zur Ramanujanschen τ-Funktion”, Arch. Math., Vol. 43, (1984), pp. 358–363. http://dx.doi.org/10.1007/BF01196660 
  6. [6] D.R. Health-Brown: “Franctional moments of the Riemann zeta-function”, J. London Math. Soc., Vol. 24(2), (1981), pp. 65–78. 
  7. [7] D. Joyner: Distribution Theorems of L-functions, Longman Scientific, Harlow, 1986. Zbl0609.10032
  8. [8] A. Kačėnas and A. Laurinčikas: “On Dirichlet series related to certain cusp forms”, Lith. Math. J., Vol. 38, (1998), pp. 64–76. http://dx.doi.org/10.1007/BF02465545 Zbl0926.11064
  9. [9] A. Laurinčikas: Limit Theorems for the Riemann Zeta-function, Kluwer, Dordrecht, 1996. 
  10. [10] A. Laurinčikas and R. Garunkštis: The Lerch Zeta-Function, Kluwer, Dordrecht, 2002. Zbl1028.11052
  11. [11] R. Leipnik: “The lognormal distribution and strong nonuniqueness of the moment problems”, Teor. Veroyatn. Primenen., Vol. 26, (1981), pp. 863–865. Zbl0474.60013
  12. [12] B.V. Levin and A.S. Fainleib: “On one method of summing of multiplicative functions”, Izv. AN SSSR, ser. matem., Vol. 31, (1967), pp. 697–710. 
  13. [13] B.V. Levin and A.S. Fainleib: “Application of certain integral equations to problems of the number theory”, Uspechi matem. nauk, Vol. 22(3), (1967), pp. 119–197. Zbl0204.06502
  14. [14] K. Matsumoto: “Probabilistic value-distribution theory of zeta-functions”, Sūgaku, Vol. 53, (2001), pp. 279–296. 
  15. [15] H.L. Montgomery and R.C. Vaughan: “Hilbert’s inequality”, J. London Math. Soc., Vol. 8(2), (1974), pp. 73–82. Zbl0281.10021
  16. [16] L. Mordell: “On Mr. Ramanujan’s empirical expansions of modular functions”, Proc. Camb. Phil. Soc., Vol. 19, (1917), pp. 117–124. Zbl46.0605.01
  17. [17] S. Ramanujan: “On certain arithmetic al functions”, it Trans. Camb. Phil. Soc., Vol. 22, (1916), pp. 159–184. 
  18. [18] R.A. Rankin: “An Ω-result for the coefficients of cusp forms”, Math. Ann., Vol. 203, (1973), pp. 239–250. http://dx.doi.org/10.1007/BF01629259 Zbl0254.10021
  19. [19] R.A. Rankin: “Ramanujan’s tau-function and its generalizations”, Ramanujan revisited (Urbana-Champaign, Ill. 1987), Academic Press, Boston, 1988, pp. 245–268. 
  20. [20] A. Selberg: “Old and new conjectures and results about a class of Dirichlet series”, Collected Papers, Vol. 2, Springer-Verlag, Berlin, 1991, pp. 47–63. 
  21. [21] G. Tenenbaum: Introduction to Analytic and Probabilistic Number Theory, Cambridge University Press, 1995. 
  22. [22] E. Wirsing: “Das asymptotische Verhalten von Summen Über multiplikative Funktionen”, Math. Ann., Vol. 143, (1961), pp. 75–102. http://dx.doi.org/10.1007/BF01351892 Zbl0104.04201

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.