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A note on Gekeler’s h-function
We give a brief introduction to Drinfeld modular forms, concentrating on the many equivalent constructions of the form h of weight q + 1 and type 1,...
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On the distribution of torsion points modulo primes: the case of function fields
We derive an analogue, in the setting of function fields, of a result (Chen–Kuan) on the distribution of torsion points in commutative algebraic...
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Dedekind sums in function fields
Okada (J Number Theory, 130:1750–1762,
2010 ) introduced Dedekind sums associated to a certain A -lattice, and established the reciprocity law. In this... -
On periods of the third kind for rank 2 Drinfeld module
In analogy with the periods of abelian integrals of differentials of the third kind for an elliptic curve defined over a number field, we introduce a...
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Action of Hecke operators on two distinguished Drinfeld modular forms
We study the action of Hecke operators on certain non-standard Fourier expansions for the Drinfeld-Eisenstein series E q -1 and the Drinfeld...
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Compactification of Drinfeld modular varieties and Drinfeld modular forms of arbitrary rank
We give an abstract characterization of the Satake compactification of a general Drinfeld modular variety. We prove that it exists and is unique up...
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Special values of Drinfeld modular forms and algebraic independence
Let A be a polynomial ring in one variable over a finite field and k be its fraction field. Let f be a Drinfeld modular form of nonzero weight for a...
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Zeta elements in the K-theory of Drinfeld modular varieties
Beilinson (Contemp Math 55:1–34,
1986 ) constructs special elements in the second K -group of an elliptic modular curve, and shows that the image under... -
A Dirichlet unit theorem for Drinfeld modules
We show that the module of integral points on a Drinfeld module satisfies an analogue of Dirichlet’s unit theorem, despite its failure to be finitely...
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Pure Anderson motives and abelian τ-sheaves
Pure t -motives were introduced by G. Anderson as higher dimensional generalizations of Drinfeld modules, and as the appropriate analogs of abelian...
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Monodromie du faisceau pervers des cycles évanescents de quelques variétés de Shimura simples
In the geometric situation of the simple Shimura varieties of Kottwitz studied in Harris and Taylor’s book (The Geometry and Cohomology of Some...
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Tannakian duality for Anderson–Drinfeld motives and algebraic independence of Carlitz logarithms
We develop a theory of Tannakian Galois groups for t -motives and relate this to the theory of Frobenius semilinear difference equations. We show that...
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Hypergeometric Functions and Carlitz Differential Equations over Function Fields
The paper is a survey of recent results in analysis of additive functions over function fields motivated by applications to various classes of...