Sturm-type bounds for modular forms over function fields

JOURNAL OF NUMBER THEORY

卷:237

Article

Armana, Cecile¹  Wei, Fu-Tsun² 

[1] Univ Bourgogne Franche Comte, Lab Math Besancon, CNRS UMR 6623, F-25030 Besancon, France

[2] Natl Tsing Hua Univ, Dept Math, 101 Sect 2,Kuang-Fu Rd, Hsinchu 30013, Taiwan

关键词: Function field;    Bruhat-Tits tree;    Harmonic cochain;    Drinfeld modular form;    Hecke operator;    Sturm bound;   

DOI  :  10.1016/j.jnt.2020.07.003

来源: Elsevier

【 摘 要 】

In this paper, we obtain two analogues of the Sturm bound for modular forms in the function field setting. In the case of mixed characteristic, we prove that any harmonic cochain is uniquely determined by an explicit finite number of its first Fourier coefficients where our bound is much smaller than the ones in the literature. A similar bound is derived for generators of the Hecke algebra on harmonic cochains. As an application, we present a computational criterion for checking whether two elliptic curves over the rational function field F-q(theta) with same conductor are isogenous. In the case of equal characteristic, we also prove that any Drinfeld modular form is uniquely determined by an explicit finite number of its first coefficients in the t-expansion. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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