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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, 29 no. 3 (2017), p. 729-753
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Class. Math.: 11F52, 11F33, 11G09
Keywords: Drinfeld modular forms, Goss polynomials, $v$-adic modular forms, hyperderivatives, false Eisenstein series

Résumé - Abstract

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.

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