Roth’s Theorem over arithmetic function
fields

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.

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On Kähler’s integral differential forms of arithmetic function fields

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ◽

10.1007/bf02941285 ◽

2003 ◽

Vol 73 (1) ◽

pp. 297-310 ◽

Cited By ~ 2

Author(s):

Ernst Kunz ◽

Rolf Waldi

Keyword(s):

Arithmetic Function ◽

Function Fields ◽

Differential Forms

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The moments and statistical distribution of class number of primes over function fields

Finite Fields and Their Applications ◽

10.1016/j.ffa.2021.101845 ◽

2021 ◽

Vol 73 ◽

pp. 101845

Author(s):

Julio Andrade ◽

Asmaa Shamesaldeen

Keyword(s):

Class Number ◽

Function Fields ◽

Statistical Distribution

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1. Finite Fields and Function Fields

Algebraic Geometry in Coding Theory and Cryptography ◽

10.1515/9781400831302-002 ◽

2010 ◽

pp. 1-29

Keyword(s):

Finite Fields ◽

Function Fields ◽

And Function

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ON THE GROWTH OF LINEAR RECURRENCES IN FUNCTION FIELDS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972720001094 ◽

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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