Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-27T02:31:00.756Z Has data issue: false hasContentIssue false
  • English
  • Français

An explicit Hecke's bound and exceptions of even unimodular quadratic forms

Published online by Cambridge University Press:  17 April 2009

Kok Seng Chua
Kok Seng Chua
Affiliation:
Institute of High Performance Computing, High End Computing Division, 1 Scenic Park Rd, #01–01 The Capricorn, Singapore Science Park II, Singapore 117528, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove an explicit Hecke's bound for the Fourier coefficients of holomorphic cusp forms for SL2(Z) and apply it to derive effectively computable constants c (m) for each dimension m, divisible by 8, for which every even integer is always represented by every even unimodular form of m variables.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 231 - 238
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Chakraborty, K., Lal, A.K. and Ramakrishnan, B., ‘Modular forms which behave like theta series’, Math. Comp. 66 (1997), 1169–1183.CrossRefGoogle Scholar
[2]Conway, J.H. and Sloane, N.J.A., Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften 290, (second edition) (Springer-Verlag, Berlin, Heidelberg, New York, 1988).CrossRefGoogle Scholar
[3]Lal, A.K. and Chakraborty, K., ‘On exceptions of integral quadratic forms’, Contemp Math. 210 (1988), 151–170.CrossRefGoogle Scholar
[4]Lang, S., Introduction to modular forms, Grundlehren der Mathematischen Wissenschaften 222 (Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[5]Odlyzko, A.M. and Sloane, N.J.A., ‘On exceptions of integral quadratic forms’, J. Reine Angew. Math. 321 (1981), 212–216.Google Scholar
[6]Peters, M., ‘Exceptions of integral quadratic forms’, J. Reine Angew. Math. 314 (1980), 196–199.Google Scholar
[7]Serre, J.P., A Course in arithmetic, Graduate Texts in Mathematics 7 (Springer-Verlag, Berlin, Heidelberg, New York, 1973).CrossRefGoogle Scholar
[8]Tartakovsky, V.A., ‘Die Gesamtheit der Zahlen, die durch eine positive quadratishe form F (x 1,…,x s) (s ≥ 4) darstellbar sind’, Izv. Akad. Nauk SSSR 7 (1929), 111–122, 165–195.Google Scholar