Nevanlinna Theory over Function Fields

2014 ◽  
pp. 341-359
Author(s):  
Junjiro Noguchi ◽  
Jörg Winkelmann
Keyword(s):  
Nevanlinna Theory ◽  
Function Fields

scholarly journals ON THE TRUNCATED SMALL FUNCTION THEOREM IN NEVANLINNA THEORY

2006 ◽  
Vol 17 (04) ◽  
pp. 417-440 ◽  
Author(s):  
KATSUTOSHI YAMANOI
Keyword(s):  
Nevanlinna Theory ◽  
Function Fields ◽  
Target Space ◽  
Small Function ◽  
Second Main Theorem ◽  
Type Estimate ◽  
Family Of Curves

We prove a second main theorem type estimate in Nevanlinna theory when a target space is a family of curves. This estimate unifies the truncated q-small function theorem, and the height inequality for curves over function fields.

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.

On geometric Z p -extensions of function fields

1988 ◽  
Vol 62 (2) ◽  
pp. 145-161 ◽  
Author(s):  
R. Gold ◽  
H. Kisilevsky
Keyword(s):  
Function Fields

scholarly journals Correction to: Divisibility problems for function fields

2020 ◽  
Vol 160 (2) ◽  
pp. 519-521
Author(s):  
S. Baier ◽  
A. Bansal ◽  
R. K. Singh
Keyword(s):  
Function Fields
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