On improvements of ther-adding walk in a finite field of characteristic 2

2016 ◽  
Vol 19 (1) ◽  
pp. 13-38
Author(s):  
Ansari Abdullah ◽  
Hardik Gajera ◽  
Ayan Mahalanobis
Keyword(s):  
Finite Field ◽  
Characteristic 2

Maximal T-spaces of free associative algebras over a finite field

2018 ◽  
Vol 17 (04) ◽  
pp. 1850064
Author(s):  
C. Bekh-Ochir ◽  
S. A. Rankin
Keyword(s):  
Finite Field ◽  
Positive Characteristic ◽  
Associative Algebras ◽  
Prime Field ◽  
Characteristic 2 ◽  
Infinite Set

In earlier work, it was established that for any finite field [Formula: see text] and any nonempty set [Formula: see text], the free associative (nonunitary) [Formula: see text]-algebra on [Formula: see text], denoted by [Formula: see text], had infinitely many maximal [Formula: see text]-spaces, but exactly two maximal [Formula: see text]-ideals (each of which was shown to be a maximal [Formula: see text]-space). This raises the interesting question as to whether or not the maximal [Formula: see text]-spaces can be classified. However, aside from the two maximal [Formula: see text]-ideals, no examples of maximal [Formula: see text]-spaces of [Formula: see text] have been identified to this point. This paper presents, for each finite field [Formula: see text], an infinite set of proper [Formula: see text]-spaces [Formula: see text] of [Formula: see text], none of which is a [Formula: see text]-ideal. It is proven that for any distinct integers [Formula: see text], [Formula: see text]. Furthermore, it is proven that for the prime field [Formula: see text], [Formula: see text] any prime, [Formula: see text] is a maximal [Formula: see text]-space of [Formula: see text]. We conjecture that for any finite field [Formula: see text] of positive characteristic different from 2 and each integer [Formula: see text], [Formula: see text] is a maximal [Formula: see text]-space of [Formula: see text]. In characteristic 2, the situation is slightly different and we provide different candidates for maximal [Formula: see text]-spaces.

scholarly journals The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2

2015 ◽  
Vol 373 (2040) ◽  
pp. 20140311 ◽  
Author(s):  
Dan Carmon
Keyword(s):  
Finite Field ◽  
Rational Function ◽  
Function Field ◽  
Möbius Function ◽  
Rational Function Field ◽  
Mobius Function ◽  
Characteristic 2

We prove a function field version of Chowla's conjecture on the autocorrelation of the Möbius function in the limit of a large finite field of characteristic 2, extending previous work in odd characteristic.

On the unitary units of the group algebra 𝔽2kQ16

2015 ◽  
Vol 08 (01) ◽  
pp. 1550013 ◽  
Author(s):  
Zahid Raza ◽  
Riasat Ali
Keyword(s):  
Finite Field ◽  
Group Algebra ◽  
Quaternion Group ◽  
Characteristic 2

In this note, the structure of unitary unit groups V*(𝔽2kQ16) is investigated, where Q16, is quaternion group of order 16, and 𝔽2k is any finite field of characteristic 2, with 2k elements. In particular, we give the center Z(V*(𝔽2kQ16)) of unitary units subgroup V*(𝔽2kQ16) of group algebra 𝔽2kQ16. The structure of the unitary unit subgroup V*(𝔽2kQ16) is described with the help of the Z(V*(𝔽2kQ16)).

ON THE UNITARY UNITS OF THE GROUP ALGEBRA 𝔽2mM16

2013 ◽  
Vol 12 (08) ◽  
pp. 1350059 ◽  
Author(s):  
ZAHID RAZA ◽  
MAQSOOD AHMAD
Keyword(s):  
Finite Field ◽  
Group Algebra ◽  
Modular Group ◽  
Characteristic 2

In this note, we have given the center Z(V*(𝔽2mM16)) of unitary units subgroup V*(𝔽2mM16) of group algebra 𝔽2mM16, where M16 = 〈x, y | x8 = y2 = 1, xy = yx5〉 is the Modular group of order 16 and 𝔽2m is any finite field of characteristic 2, with 2m elements. The structure of the unitary unit subgroup V*(𝔽2mM16) of the group algebra 𝔽2mM16, is also described, see Theorem 3.1.

The analog of the Erdös distance problem in finite fields

2017 ◽  
Vol 13 (09) ◽  
pp. 2319-2333
Author(s):  
S. D. Adhikari ◽  
Anirban Mukhopadhyay ◽  
M. Ram Murty
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Kloosterman Sums ◽  
Vector Spaces ◽  
Characteristic 2 ◽  
Distance Problem ◽  
Erdős Distance Problem ◽  
Erdos Distance Problem

In this paper, we give a proof of the result of Iosevich and Rudnev [Erdös distance problem in vector spaces over finite fields, Trans. Amer. Math. Soc. 359 (2007) 6127–6142] on the analog of the Erdös–Falconer distance problem in the case of a finite field of characteristic [Formula: see text], where [Formula: see text] is an odd prime, without using estimates for Kloosterman sums. We also address the case of characteristic 2.

scholarly journals Principal indecomposable modules for some three-dimensional special linear groups

1980 ◽  
Vol 22 (3) ◽  
pp. 439-455 ◽  
Author(s):  
James Archer
Keyword(s):  
Finite Field ◽  
Linear Group ◽  
Three Dimensional ◽  
Special Linear Group ◽  
Linear Groups ◽  
Indecomposable Modules ◽  
Special Linear ◽  
Special Linear Groups ◽  
Irreducible Modules ◽  
Characteristic 2

Let k be a finite field of characteristic 2, and let G be the three dimensional special linear group over k. The principal indecomposable modules of G over k are constructed from tensor products of the irreducible modules, and formulae for their dimensions are given.

ON THE STRUCTURE OF THE UNITARY SUBGROUP OF THE GROUP ALGEBRA 𝔽2qD2n

2014 ◽  
Vol 13 (04) ◽  
pp. 1350139 ◽  
Author(s):  
ZAHID RAZA ◽  
MAQSOOD AHMAD
Keyword(s):  
Finite Field ◽  
Group Algebra ◽  
Dihedral Group ◽  
Characteristic 2 ◽  
Unitary Subgroup

We discuss the structure of the unitary subgroup V*(𝔽2qD2n) of the group algebra 𝔽2qD2n, where D2n = 〈x, y | x2n-1 = y2 = 1, xy = yx2n-1-1〉 is the dihedral group of order 2n and 𝔽2q is any finite field of characteristic 2, with 2q elements. We will prove that [Formula: see text], see Theorem 3.1.

G2 Examples: Construction in Characteristic Two

2012 ◽  
Author(s):  
Nicholas M. Katz
Keyword(s):  
Fixed Point ◽  
Finite Field ◽  
Mellin Transform ◽  
Characteristic 2 ◽  
Characteristic Two

This chapter treats the case of characteristic two separately because it is somewhat simpler than the case of odd characteristic. Recall from the first paragraph of Chapter 25 that for k a finite field of characteristic 2, and any character χ‎ of kË£, the Tate-twisted Kloosterman sheaf of rank seven has G geom = G arith = Gâ‚‚. The first task is to express its stalk at a fixed point a É› kË£ as the finite field Mellin transform of the desired object N(a; k).

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