Abstract
We show that a certain family of the coefficients of a Drinfeld-Goss modular form with certain power eigenvalues for the Hecke operators at degree 1 primes the can be expressed as polynomial multiples of the first possible non-zero coefficient of that form. Along the way, we obtain some interesting combinatorial properties regarding difference operators in finite characteristic.
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Armana, C: Coefficients of Drinfeld modular forms and Hecke operators. J. Number Theory. 131(8), 1435–1460 (2011).
Gekeler, E-U: On the coefficients of Drinfeld modular forms. Invent. Math. 93, 667–700 (1988).
Goss, D: Modular forms for \(\mathbb {F}_{r} [t]\). J. Reine Angew. Math. 317, 16–39 (1980).
Goss, D: π-adic Eisenstein series for function fields. Compositio Math. 41(1), 3–38 (1980).
Petrov, A: A-expansions of Drinfeld modular forms. J. Number Theory. 133(7), 2247–2266 (2013). doi:10.1016/j.jnt.2012.12.012.
Sage Mathematics Software (Version 4.8), The Sage Developers, (2014). http://www.sagemath.org.
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El-Guindy, A., Petrov, A. On certain coefficients of Drinfeld-Goss eigenforms with power eigenvalues. Res. number theory 2, 10 (2016). https://doi.org/10.1007/s40993-015-0034-2
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DOI: https://doi.org/10.1007/s40993-015-0034-2