scholarly journals On the Burau representation of B4 modulo p

2021 ◽  
pp. 57-62
Author(s):  
A. Beridze ◽  
S. Bigelow ◽  
P. Traczyk
Keyword(s):  
Burau Representation ◽  
Modulo P

scholarly journals Solutions of KZ differential equations modulo p

2018 ◽  
Vol 48 (3) ◽  
pp. 655-683 ◽  
Author(s):  
Vadim Schechtman ◽  
Alexander Varchenko
Keyword(s):  
Differential Equations ◽  
Modulo P

scholarly journals The Interplay between Linear Representations of the Braid Group

2007 ◽  
Vol 2007 ◽  
pp. 1-9
Author(s):  
Mohammad N. Abdulrahim ◽  
Nibal H. Kassem
Keyword(s):  
Free Group ◽  
Braid Group ◽  
Burau Representation ◽  
Standard Representation ◽  
Linear Representations ◽  
Standard Action ◽  
Composition Factors

We consider Wada's representation as a twisted version of the standard action of the braid group,Bn, on the free group withngenerators. Constructing a free group,Gnm, of ranknm, we compose Cohen's mapBn→Bnmand the embeddingBnm→Aut(Gnm)via Wada's map. We prove that the composition factors of the obtained representation are one copy of Burau representation andm−1copies of the standard representation after changing the parameterttotkin the definitions of the Burau and standard representations. This is a generalization of our previous result concerning the standard Artin representation of the braid group.

scholarly journals On the number of prime divisors of the order of elliptic curves modulo p

2005 ◽  
Vol 117 (4) ◽  
pp. 341-352 ◽  
Author(s):  
Jörn Steuding ◽  
Annegret Weng
Keyword(s):  
Elliptic Curves ◽  
Prime Divisors ◽  
Modulo P ◽  
Number Of Prime Divisors

scholarly journals Generator of PRN's on the norm group

2021 ◽  
Vol 25 (2(36)) ◽  
pp. 26-39
Author(s):  
P. Fugelo ◽  
S. Varbanets
Keyword(s):  
Prime Number ◽  
Quadratic Field ◽  
Exponential Sum ◽  
Random Numbers ◽  
Gaussian Integers ◽  
New Family ◽  
Serial Test ◽  
Polynomial Representations ◽  
Modulo P ◽  
Norm Group

Let $p$ be a prime number, $d\in\mathds{N}$, $\left(\frac{-d}{p}\right)=-1$, $m>2$, and let $E_m$ denotes the set of of residue classes modulo $p^m$ over the ring of Gaussian integers in imaginary quadratic field $\mathds{Q}(\sqrt{-d})$ with norms which are congruented with 1 modulo $p^m$. In present paper we establish the polynomial representations for real and imagimary parts of the powers of generating element $u+iv\sqrt{d}$ of the cyclic group $E_m$. These representations permit to deduce the ``rooted bounds'' for the exponential sum in Turan-Erd\"{o}s-Koksma inequality. The new family of the sequences of pseudo-random numbers that passes the serial test on pseudorandomness was being buit.

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