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Article Dans Une Revue Journal of Number Theory Année : 2022

Sturm-type bounds for modular forms over functions fields

Résumé

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 $\mathbb{F}_{q}(\theta)$ 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.
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Dates et versions

hal-02493616 , version 1 (28-02-2020)
hal-02493616 , version 2 (20-08-2020)

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Citer

Cécile Armana, Fu-Tsun Wei. Sturm-type bounds for modular forms over functions fields. Journal of Number Theory, 2022, 237, pp.67-98. ⟨10.1016/j.jnt.2020.07.003⟩. ⟨hal-02493616v2⟩
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