15 citations · 64 across the 25 of their papers we have counts for
14 papers · 1 filter
Algebraic independence of periods of Anderson modules and their hyperderivatives
Andreas Maurischat, Changningphaabi Namoijam
Transcendence questions of periods and quasi-periods of Anderson modules, as well as the hyperderivatives thereof, are of major interest in number theory over function fields. In t…
On purity of Anderson t-modules
Yen-Tsung Chen, Andreas Maurischat
In the theory of abelian Anderson -modules, pure Anderson -modules play an important role. Namoijam and Papanikolas also introduced the notions of strictly pure and almost st…
Determining -motives and dual -motives in Anderson's theory
Andreas Maurischat
Anderson t-modules are analogs of abelian varieties in positive characteristic. Associated to such a t-module, there are its t-motive and its dual t-motive. When dealing with these…
Non-abelian Anderson A-modules: Comparison isomorphisms and Galois representations
Andreas Maurischat
In this manuscript, we consider non-abelian Anderson -modules (of generic characteristic). The main results are on the structure of their motives, and on comparison isomorph…
Residue of special functions of Anderson -modules at the characteristic graph
Quentin Gazda, Andreas Maurischat
Let be an Anderson -module over . The period lattice of is related to its module of special functions by means of a non-canonical isomorphism introd…
Abelian equals A-finite for Anderson A-modules
Andreas Maurischat
Anderson introduced t-modules as higher dimensional analogs of Drinfeld modules. Attached to such a t-module, there are its t-motive and its dual t-motive. The t-module gets the at…
Algebraic independence of the Carlitz period and its hyperderivatives
Andreas Maurischat
This paper deals with the fundamental period of the Carlitz module. The main theorem states that the Carlitz period and all its hyperderivatives are algebraically indepen…
Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions
Andreas Maurischat, Rudolph Perkins
We generalize our work on Carlitz prime power torsion extension to torsion extensions of Drinfeld modules of arbitrary rank. As in the Carlitz case, we give a description of these…
Anderson t-modules with thin t-adic Galois representations
Andreas Maurischat
Pink has given a qualitative answer to the Mumford-Tate conjecture for Drinfeld modules in the 90s. He showed that the image of the v-adic Galois representation is v-adically open…
On field extensions given by periods of Drinfeld modules
Andreas Maurischat
In this short note, we answer a question raised by M. Papikian on a universal upper bound for the degree of the extension of given by adjoining the periods of a Drinfeld…
Special Functions and Gauss-Thakur Sums in Higher Rank and Dimension
Quentin Gazda, Andreas Maurischat
Anderson generating functions have received a growing attention in function field arithmetic in the last years. Despite their introduction by Anderson in the 80s where they were at…
Periods of -modules as special values
Andreas Maurischat
In this article we show that all periods of uniformizable -modules (resp. their coordinates) can be obtained via specializing a rigid analytic trivialization of a related dual $…
Prolongations of t-motives and algebraic independence of periods
Andreas Maurischat
In this article we show that the coordinates of a period lattice generator of the -th tensor power of the Carlitz module are algebraically independent, if is prime to the ch…
An Integral Digit Derivative Basis for Carlitz Prime Power Torsion Extensions
Andreas Maurischat, Rudolph Perkins
Let be a monic irreducible polynomial in , the ring of polynomials in the indeterminate over the finite field , and let be…