scholarly journals The large sieve inequality with square moduli for quadratic extensions of function fields

2020 ◽  
Vol 16 (09) ◽  
pp. 1907-1922
Author(s):  
Stephan Baier ◽  
Rajneesh Kumar Singh
Keyword(s):  
Rational Function ◽  
Function Fields ◽  
Large Sieve ◽  
Quadratic Extensions ◽  
Large Sieve Inequality

In this paper, we establish a version of the large sieve inequality with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.

scholarly journals Large sieve inequality with power moduli for function fields

2019 ◽  
Vol 196 ◽  
pp. 1-13 ◽  
Author(s):  
Stephan Baier ◽  
Rajneesh Kumar Singh
Keyword(s):  
Function Fields ◽  
Large Sieve ◽  
Large Sieve Inequality

scholarly journals LARGE SIEVE INEQUALITY WITH CHARACTERS FOR POWERFUL MODULI

2005 ◽  
Vol 01 (02) ◽  
pp. 265-279 ◽  
Author(s):  
STEPHAN BAIER ◽  
LIANGYI ZHAO
Keyword(s):  
General Formula ◽  
Large Sieve ◽  
Large Sieve Inequality

In this paper we aim to generalize the results in [1, 2, 19] and develop a general formula for large sieve with characters to powerful moduli that will be an improvement to the result in [19].

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
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