Theta operators, Goss polynomials, and v-adic modular forms
Matthew A. Papanikolas1; Guchao Zeng1
1 Department of Mathematics Texas A&M University College Station, TX 77843, USA
Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 729-753.

We investigate hyperderivatives of Drinfeld modular forms and determine formulas for these derivatives in terms of Goss polynomials for the kernel of the Carlitz exponential. As a consequence we prove that v-adic modular forms in the sense of Serre, as defined by Goss and Vincent, are preserved under hyperdifferentiation. Moreover, upon multiplication by a Carlitz factorial, hyperdifferentiation preserves v-integrality.

Nous étudions les dérivées divisées des formes modulaires de Drinfeld et déterminons des formules pour ces dérivées en termes de polynômes de Goss pour le noyau de l’exponentielle de Carlitz. Comme conséquence, nous prouvons que les dérivées divisées des formes modulaires v-adiques au sens de Serre, définies par Goss et Vincent, sont encore des formes modulaires v-adiques. De plus, à multiplication par une factorielle de Carlitz près, la v-intégralité est stable sous les opérateurs de dérivation divisée.

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.999
Classification: 11F52, 11F33, 11G09
Mots-clés : Drinfeld modular forms, Goss polynomials, $v$-adic modular forms, hyperderivatives, false Eisenstein series

Matthew A. Papanikolas 1; Guchao Zeng 1

1 Department of Mathematics Texas A&M University College Station, TX 77843, USA
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Matthew A. Papanikolas; Guchao Zeng. Theta operators, Goss polynomials, and $v$-adic modular forms. Journal de théorie des nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 729-753. doi : 10.5802/jtnb.999. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.999/

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