Airy矩的Hodge性质

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2021-12-26 DOI:10.2140/tunis.2023.5.215
C. Sabbah, Jeng-Daw Yu
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引用次数: 2

摘要

我们考虑三次指数和的对称幂矩的复类似物。这些是经典艾里微分方程的对称幂。我们证明了他们的de Rham上同调是Anderson意义上的算术Hodge结构的基础,并且我们通过由有理数索引的不规则Hodge滤波来计算他们的Hodge数,在他们实现为指数混合Hodge结构时。主要结果是所有的霍奇数要么是零要么是一。
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Hodge properties of Airy moments
We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
期刊最新文献
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