scholarly journals Quadratic forms over rational function fields in characteristic 2

2006 ◽  
Vol 228 (1) ◽  
pp. 19-51 ◽  
Author(s):  
Roberto Aravire ◽  
Bill Jacob
Keyword(s):  
Rational Function ◽  
Quadratic Forms ◽  
Function Fields ◽  
Characteristic 2

scholarly journals The algebraic closure in function fields of quadratic forms in characteristic 2

1997 ◽  
Vol 55 (2) ◽  
pp. 293-297 ◽  
Author(s):  
Hamza Ahmad
Keyword(s):  
Quadratic Form ◽  
Function Field ◽  
Quadratic Forms ◽  
Function Fields ◽  
Algebraic Closure ◽  
Characteristic 2 ◽  
Characteristic Two

For a field k of characteristic not two, it is known that k is algebraically closed in the function field of any (non-degenerate) quadratic form in three or more variables. In this note we consider fields of characteristic two and decide when k is algebraically closed in a function field of a quadratic k-form. For quadratic forms in three variables this has recently been done by Ohm.

scholarly journals Pencils of Quadratic Forms and Hyperelliptic Function Fields

2000 ◽  
Vol 227 (2) ◽  
pp. 532-548
Author(s):  
David B. Leep ◽  
Laura Mann Schueller
Keyword(s):  
Quadratic Forms ◽  
Function Fields ◽  
Hyperelliptic Function

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].

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