Comparison of integral structures on the space of modular forms of full level N

IF 0.6 3区 数学 Q3 MATHEMATICS
Anthony Kling
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引用次数: 0

Abstract

Let N3 and r1 be integers and p2 be a prime such that pN. One can consider two different integral structures on the space of modular forms over Q, one coming from arithmetic via q-expansions, the other coming from geometry via integral models of modular curves. Both structures are stable under the Hecke operators; furthermore, their quotient is finite torsion. Our goal is to investigate the exponent of the annihilator of the quotient. We will apply methods due to Brian Conrad to the situation of modular forms of even weight and level Γ(Npr) over Qp(ζNpr) to obtain an upper bound for the exponent. We also use Klein forms to construct explicit modular forms of level pr whenever pr>3, allowing us to compute a lower bound which agrees with the upper bound. Hence we compute the exponent precisely.

全级 N 模形式空间积分结构的比较
设 N≥3 和 r≥1 为整数,p≥2 为质数,使得 p∤N 。我们可以在 Q 上的模形式空间上考虑两种不同的积分结构,一种来自算术的 q 展开,另一种来自几何的模态曲线积分模型。这两种结构在赫克算子作用下都是稳定的;此外,它们的商都是有限扭转的。我们的目标是研究商的湮没器指数。我们将把布莱恩-康拉德(Brian Conrad)的方法应用于 Qp(ζNpr) 上偶数权重和级Γ(Npr) 的模形式,从而得到指数的上界。我们还利用克莱因形式构建了每当pr>3 时pr 级的显式模块形式,从而计算出与上界一致的下界。因此,我们可以精确地计算指数。
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来源期刊
Journal of Number Theory
Journal of Number Theory 数学-数学
CiteScore
1.30
自引率
14.30%
发文量
122
审稿时长
16 weeks
期刊介绍: The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
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