On Kähler’s integral differential forms of arithmetic function fields

2003 ◽  
Vol 73 (1) ◽  
pp. 297-310 ◽  
Author(s):  
Ernst Kunz ◽  
Rolf Waldi
Keyword(s):  
Arithmetic Function ◽  
Function Fields ◽  
Differential Forms

scholarly journals Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields

2019 ◽  
Vol 372 (8) ◽  
pp. 5263-5286
Author(s):  
J.-L. Colliot-Thélène ◽  
D. Harbater ◽  
J. Hartmann ◽  
D. Krashen ◽  
R. Parimala ◽  
...  
Keyword(s):  
Homogeneous Spaces ◽  
Arithmetic Function ◽  
Function Fields ◽  
Global Principles

scholarly journals Local-global Galois theory of arithmetic function fields

2019 ◽  
Vol 232 (2) ◽  
pp. 849-882
Author(s):  
David Harbater ◽  
Julia Hartmann ◽  
Daniel Krashen ◽  
Raman Parimala ◽  
Venapally Suresh
Keyword(s):  
Galois Theory ◽  
Arithmetic Function ◽  
Function Fields

ABEL ARITHMETIC FUNCTIONS IN FINITE CHARACTERISTIC

2012 ◽  
Vol 08 (06) ◽  
pp. 1557-1568
Author(s):  
DAVID ADAM
Keyword(s):  
Exponential Type ◽  
Positive Characteristic ◽  
Arithmetic Function ◽  
Function Fields ◽  
Arithmetic Functions ◽  
Finite Characteristic

We define Abel arithmetic functions in function fields with positive characteristic. We prove that any Abel arithmetic function with exponential type lesser than [Formula: see text] is a polynomial, the bound [Formula: see text] being optimal. This provides an analog of a Bertrandias' result. Some q-analogs are considered too.

scholarly journals ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

2020 ◽  
pp. 1-10
Author(s):  
CLEMENS FUCHS ◽  
SEBASTIAN HEINTZE
Keyword(s):  
Number Field ◽  
Function Field ◽  
Function Fields ◽  
Linear Recurrence ◽  
Recurrence Sequence ◽  
Linear Recurrences ◽  
Field Case ◽  
Power Sum ◽  
Linear Recurrence Sequence

Abstract Let $ (G_n)_{n=0}^{\infty } $ be a nondegenerate linear recurrence sequence whose power sum representation is given by $ G_n = a_1(n) \alpha _1^n + \cdots + a_t(n) \alpha _t^n $ . We prove a function field analogue of the well-known result in the number field case that, under some nonrestrictive conditions, $ |{G_n}| \geq ( \max _{j=1,\ldots ,t} |{\alpha _j}| )^{n(1-\varepsilon )} $ for $ n $ large enough.

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