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

El-Guindy, Ahmad; Petrov, Aleksandar

doi:10.1090/proc/12406

On symmetric powers of $\tau$-recurrent sequences and deformations of Eisenstein series
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by Ahmad El-Guindy and Aleksandar Petrov

Proc. Amer. Math. Soc. 143 (2015), 3303-3318

DOI: https://doi.org/10.1090/proc/12406

Published electronically: April 28, 2015

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Abstract:

We prove the equality of several $\tau$-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; and a new proof of relations between special values of Pellarin $L$-series.

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