Planes in $\mathbb{Z^4}$ and Eisenstein series

Gautam Chinta; Valdir Pereira Júnior

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arXiv · 2110.13997

Planes in $\mathbb{Z^4}$ and Eisenstein series

Gautam Chinta·Valdir Pereira Júnior

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Abstract

We study the number of two-dimensional sublattices of $\mathbb{Z^4}$ of a fixed covolume and construct the associated Dirichlet series. The latter is shown to be related to Eisenstein series on both $GL_4$ and its metaplectic double cover.

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Gautam Chinta, Valdir Pereira Júnior. 2021-10-26. Planes in $\mathbb{Z^4}$ and Eisenstein series. https://arxiv.org/abs/2110.13997

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