39
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

How to Compute the Coefficients of the Elliptic Modular Function j(z)

&
Pages 115-121 | Published online: 03 Apr 2012

REFERENCES

  • Baier , H. 2002 . “Efficient Algorithms for Generating Elliptic Curves over Finite Fields Suitable for Use in Cryptography.” , PhD thesis Darmstadt University of Technology. . [Baier 02]
  • Gouvûa , F. Q. 1997 . “Non-Ordinary Primes: A Story.” . Exp. Math. , 6 ( 3 ) : 195 – 205 . [Gouvêa 97]
  • Herrmann , O. 1973 . “Über die Berechnung der Fourierkoeffizienten der Funktion j(T).” . J. f. d. reine u. angew. Math. , 274 : 187 – 195 . [Herrmann 73]
  • Kaneko , M. 1999 . Traces of Singular Moduli and the Fourier Coefficients of the Elliptic Modular Function j(τ). [Kaneko 99], Volume 19 of Number Theory. Fifth Conf. Canad. Number Theory Assoc., Ottawa, Ontario, Canada, Aug. 1996. AMS, CRM Proc. Lect. Notes
  • Köhler , G. 1988 . “Theta Series on the Hecke Groups G(√2) and G(√3).” . Math. Z. , 197 ( 1 ) : 69 – 96 . [Köhler 88]
  • Knopp , M. 1990 . “Rademacher on J(τ), Poincaré Series of Nonpositive Weights and the Eichler Cohomology.” . Notices Amer. Math. Soc. , 37 : 385 – 393 . [Knopp 90]
  • Mahler , K. 1976 . “On a Class of Non-Linear Functional Equations Connected with Modular Functions.” . Journal of the Australian Mathematical Society , 22 : 65 – 120 . [Mahler 76], Series A
  • Niebur , D. 1975 . “A Formula for Ramanujan's τ- Function.” . Ill. J. Math. , 19 : 448 – 449 . [Niebur 75]
  • Rademacher , H. 1938 . “The Fourier Coefficients of the Modular Invariant J(τ).” . Amer. J. Math. , 60 : 501 – 512 . [Rademacher 38]
  • Ramanujan , S. 1927 . Collected Papers. Cambridge , , UK : Cambridge University Press. . [Ramanujan 27], Reprinted New York, 1962
  • Schoeneberg , B. 1953 . “Über den Zusammenhang der Eisensteinschen Reihen und Thetareihen mit der Diskriminante der elliptischen Funktionen.” . Math. Ann. , 126 : 177 – 184 . [Schoeneberg 53]
  • Serre , J. P. 1985 . “Sur la lacunarite des puissances de e.” . Glasg. Math. J. , 27 : 203 – 221 . [Serre 85]
  • Zagier , D. 1996 . “Traces of Singular Moduli.” [Zagier 96], preprint, Preprint

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.