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2013 An analogue of Sturm's theorem for Hilbert modular forms
Yuuki Takai
Algebra Number Theory 7(4): 1001-1018 (2013). DOI: 10.2140/ant.2013.7.1001


In this paper, we consider congruences of Hilbert modular forms. Sturm showed that mod elliptic modular forms of weight k and level Γ1(N) are determined by the first (k12)[Γ1(1):Γ1(N)] mod Fourier coefficients. We prove an analogue of Sturm’s result for Hilbert modular forms associated to totally real number fields. The proof uses the positivity of ample line bundles on toroidal compactifications of Hilbert modular varieties.


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Yuuki Takai. "An analogue of Sturm's theorem for Hilbert modular forms." Algebra Number Theory 7 (4) 1001 - 1018, 2013.


Received: 22 November 2011; Revised: 30 August 2012; Accepted: 4 September 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1330.11030
MathSciNet: MR3095234
Digital Object Identifier: 10.2140/ant.2013.7.1001

Primary: 11F41
Secondary: 11F30 , 11F33 , 14C17

Keywords: congruences of modular forms , Hilbert modular forms and varieties , intersection numbers , Sturm's theorem , toroidal and minimal compactifications

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 4 • 2013
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