arXiv Open Access 2024

On the third kind periods for abelian $t$-modules

Yen-Tsung Chen Changningphaabi Namoijam

Lihat Sumber

Abstrak

Inspired by the relations between periods of elliptic integrals of the third kind and the periods of the extensions of the corresponding elliptic curves by the multiplicative group, we introduce the notion of the third kind periods for abelian $t$-modules and establish an evaluation for these periods that is parallel to the classical setting. When we specialize our result to the case of Drinfeld modules, an explicit formula for these third kind periods is established. We also prove the algebraic independence of periods of the first, the second, and the third kind for Drinfeld modules of arbitrary rank. This generalizes prior results of Chang for rank $2$ Drinfeld modules.

Topik & Kata Kunci

math.NT

Penulis (2)

Yen-Tsung Chen

Changningphaabi Namoijam

Format Sitasi

APA MLA BibTeX

Chen, Y., Namoijam, C. (2024). On the third kind periods for abelian $t$-modules. https://arxiv.org/abs/2408.11998

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓