## The classical umbral calculus and the flow of a Drinfeld module

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- by Nguyen Ngoc Dong Quan PDF
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**369**(2017), 1265-1289 Request permission

## Abstract:

David Goss developed a very general Fourier transform in additive harmonic analysis in the function field setting. In order to introduce the Fourier transform for continuous characteristic $p$-valued functions on $\mathbb {Z}_p$, Goss introduced and studied an analogue of flows in finite characteristic. In this paper, we use another approach to study flows in finite characteristic. We recast the notion of a flow in the language of the classical umbral calculus, which allows us to generalize the formula for flows first proved by Goss to a more general setting. We study duality between flows using the classical umbral calculus, and show that the duality notion introduced by Goss seems to be a natural one. We also formulate a question of Goss about the exact relationship between two flows of a Drinfeld module in the language of the classical umbral calculus, and give a partial answer to it.## References

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## Additional Information

**Nguyen Ngoc Dong Quan**- Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
- Address at time of publication: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556
- Email: dongquan.ngoc.nguyen@gmail.com, dongquan.ngoc.nguyen@nd.edu
- Received by editor(s): July 3, 2014
- Received by editor(s) in revised form: May 25, 2015
- Published electronically: September 27, 2016
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 1265-1289 - MSC (2010): Primary 05A40, 11G09
- DOI: https://doi.org/10.1090/tran/6763
- MathSciNet review: 3572273