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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]
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Abstract

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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