### 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 lth power (1 ≤ l ≤ 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.

Original language | English |
---|---|

Pages (from-to) | 3303-3318 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 143 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

- A-expansions
- Deformations of Eisenstein series
- Vectorial Drinfeld modular forms
- τ-recurrent sequences

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*143*(8), 3303-3318. https://doi.org/10.1090/proc/12406

**On symmetric powers of τ-recurrent sequences and deformations of eisenstein series.** / ElGuindy, Ahmad; Petrov, Aleksandar.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 143, no. 8, pp. 3303-3318. https://doi.org/10.1090/proc/12406

}

TY - JOUR

T1 - On symmetric powers of τ-recurrent sequences and deformations of eisenstein series

AU - ElGuindy, Ahmad

AU - Petrov, Aleksandar

PY - 2015

Y1 - 2015

N2 - 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 lth power (1 ≤ l ≤ 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.

AB - 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 lth power (1 ≤ l ≤ 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.

KW - A-expansions

KW - Deformations of Eisenstein series

KW - Vectorial Drinfeld modular forms

KW - τ-recurrent sequences

UR - http://www.scopus.com/inward/record.url?scp=84929431312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929431312&partnerID=8YFLogxK

U2 - 10.1090/proc/12406

DO - 10.1090/proc/12406

M3 - Article

VL - 143

SP - 3303

EP - 3318

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -