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arXiv · 1305.2573

On symmetric powers of $τ$-recurrent sequences and deformations of Eisenstein series

Ahmad El-Guindy·Aleksandar Petrov
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Abstract

We prove the equality of several $τ$-recurrent sequences, which were first considered by Pellarin, and which have close connections to Drinfeld vectorial modular forms. Our result has several consequences: an $A$-expansion for the $l^\text{th}$ power ($1 \leq l \leq q$) of the deformation of the weight 2 Eisenstein series; relations between Drinfeld modular forms with $A$-expansions; a new proof of relations between special values of Pellarin $L$-series.

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Ahmad El-Guindy, Aleksandar Petrov. 2013-10-13. On symmetric powers of $τ$-recurrent sequences and deformations of Eisenstein series. https://arxiv.org/abs/1305.2573

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