scholarly journals Galois closures of quartic subfields of rational function fields

2014 ◽  
Vol 26 ◽  
pp. 100-103 ◽  
Author(s):  
Robert C. Valentini
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Galois Closures

scholarly journals Extremal behaviour of ± 1-valued completely multiplicative functions in function fields

2021 ◽  
Vol 56 (1) ◽  
pp. 79-94
Author(s):  
Nikola Lelas ◽  
Keyword(s):  
Rational Function ◽  
Finite Fields ◽  
Function Fields ◽  
Mean Value ◽  
Multiplicative Functions ◽  
Irreducible Polynomials ◽  
Liouville Function ◽  
The Mean

We investigate the classical Pólya and Turán conjectures in the context of rational function fields over finite fields 𝔽q. Related to these two conjectures we investigate the sign of truncations of Dirichlet L-functions at point s=1 corresponding to quadratic characters over 𝔽q[t], prove a variant of a theorem of Landau for arbitrary sets of monic, irreducible polynomials over 𝔽q[t] and calculate the mean value of certain variants of the Liouville function over 𝔽q[t].

scholarly journals New Binary Codes From Rational Function Fields

2015 ◽  
Vol 61 (1) ◽  
pp. 60-65 ◽  
Author(s):  
Lingfei Jin ◽  
Chaoping Xing
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Binary Codes

Simple Algebras Over Rational Function Fields

1979 ◽  
Vol 31 (4) ◽  
pp. 831-835 ◽  
Author(s):  
T. Nyman ◽  
G. Whaples
Keyword(s):  
Rational Function ◽  
Number Field ◽  
Matrix Algebra ◽  
Function Fields ◽  
Simple Algebra ◽  
Noether Theorem ◽  
Full Matrix ◽  
Full Matrix Algebra ◽  
Rank One ◽  
Simple Algebras

The well-known Hasse-Brauer-Noether theorem states that a simple algebra with center a number field k splits over k (i.e., is a full matrix algebra) if and only if it splits over the completion of k at every rank one valuation of k. It is natural to ask whether this principle can be extended to a broader class of fields. In particular, we prove here the following extension.

On subfields of rational function fields

1984 ◽  
Vol 42 (2) ◽  
pp. 136-138 ◽  
Author(s):  
Jack Ohm
Keyword(s):  
Rational Function ◽  
Function Fields

Defining transcendentals in function fields

2002 ◽  
Vol 67 (3) ◽  
pp. 947-956 ◽  
Author(s):  
Jochen Koenigsmann
Keyword(s):  
Rational Function ◽  
Function Field ◽  
Function Fields ◽  
Algebraic Closure ◽  
Rational Function Field ◽  
First Order

AbstractGiven any field K, there is a function field F/K in one variable containing definable transcendental over K, i.e., elements in F / K first-order definable in the language of fields with parameters from K. Hence, the model-theoretic and the field-theoretic relative algebraic closure of K in F do not coincide. E.g., if K is finite, the model-theoretic algebraic closure of K in the rational function field K(t) is K(t).For the proof, diophantine ∅-definability ofK in F is established for any function field F/K in one variable, provided K is large, or K× /(K×)n is finite for some integer n > 1 coprime to char K.

Distributions on rational function fields

1981 ◽  
Vol 256 (4) ◽  
pp. 549-560 ◽  
Author(s):  
Steven Galovich ◽  
Michael Rosen
Keyword(s):  
Rational Function ◽  
Function Fields
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