Brauer groups of rational function fields over global fields

1981 ◽  
pp. 46-74 ◽  
Author(s):  
B. Fein ◽  
M. Schacher
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Brauer Groups ◽  
Global Fields

scholarly journals Brauer groups of rational function fields

1979 ◽  
Vol 1 (5) ◽  
pp. 766-769 ◽  
Author(s):  
Burton Fein ◽  
Murray Schacher ◽  
Jack Sonn
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Brauer Groups

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

scholarly journals Vanishing of Massey Products and Brauer Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 730-740 ◽  
Author(s):  
Ido Efrat ◽  
Eliyahu Matzri
Keyword(s):  
Prime Number ◽  
Galois Cohomology ◽  
Brauer Groups ◽  
Central Simple Algebras ◽  
Massey Products ◽  
Global Fields ◽  
Root Of Unity ◽  
Simple Algebras ◽  
Central Simple

AbstractLet p be a prime number and F a field containing a root of unity of order p. We relate recent results on vanishing of triple Massey products in the mod-p Galois cohomology of F, due to Hopkins, Wickelgren, Mináč, and Tân, to classical results in the theory of central simple algebras. We prove a stronger form of the vanishing property for global fields.

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