Access the full text.
Sign up today, get DeepDyve free for 14 days.
P. Humbert (1939)
Théorie de la réduction des formes quadratiques définies positives dans un corps algébriqueK finiCommentarii Mathematici Helvetici, 12
K. Ramanathan (1961)
Quadratic forms over involutorial division algebras IIMathematische Annalen, 143
C. Siegel (1944)
On the Theory of Indefinite Quadratic FormsAnnals of Mathematics, 45
S. Raghavan (1962)
On representation by hermitian formsActa Arithmetica, 8
S. Raghavan (1959)
Modular Forms of Degree n and Representation by Quadratic FormsAnnals of Mathematics, 70
M. Koecher (1953)
Über Dirichlet-Reihen mit Funktionalgleichung.Journal für die reine und angewandte Mathematik (Crelles Journal), 1953
Sunder Lal (1965)
On the Fourier coefficients of Hilbert-Siegel modular formsMathematische Zeitschrift, 88
Pyatesky Sapiro (1956)
I.I. Singular modular functionsIzv. Akad. Nauk SSSR, Ser. Math., 20
By S. RAGI~VAN Let /(Z) be a modular form of degree n > 1 and weight k > 0 belonging to a principal congruence subgroup of stufe s of the Siegel modular group of degree n (see [2], [4]) and let /(g) =- ~. a(T) e ~Ltr(TZ) T>_O where T runs over n-rowed semi-integral non-negative matrices, be its Fourier expansion. If f(Z) is either an 'Eisenstein series' or a 'cusp form', there exists an estimate for the Fourier coefficients a(T) which involves the discriminant 5 (T) of T. Otherwise, for general ](Z), there exists for T ~ 0, an estimate for a(T) involving 5(T), only for k > n-~ 1 and only when T 'tends to infinity' in a special manner as described in [4]. The object of this note is to obtain an estimate for a(T) uniformly in T as the determinant of T tends to infinity and without requiring that k > n § 1. Since, e~en for subgroups of the Siegel modular group there exist for 0 < /c _< n § 1, n ~ 3 modular forms of weight/c, our theorem seems to be not without interest. The estimate that we obtain, however, is not
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Dec 3, 2013
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.