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arXiv · 1605.04235

Theta operators, Goss polynomials, and v-adic modular forms

Matthew A. Papanikolas·Guchao Zeng
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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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Matthew A. Papanikolas, Guchao Zeng. 2016-05-13. Theta operators, Goss polynomials, and v-adic modular forms. https://arxiv.org/abs/1605.04235

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