All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 10 Next

Displaying 181 – 200 of 497

Showing per page

Interpolation of hypergeometric ratios in a global field of positive characteristic

Greg W. Anderson (2007)

Annales de l’institut Fourier

For each global field of positive characteristic we exhibit many examples of two-variable algebraic functions possessing properties consistent with a conjectural refinement of the Stark conjecture in the function field case recently proposed by the author. All the examples are Coleman units. We obtain our results by studying rank one shtukas in which both zero and pole are generic, i. e., shtukas not associated to any Drinfeld module.

Irreducibility of the iterates of a quadratic polynomial over a field

Mohamed Ayad, Donald L. McQuillan (2000)

Acta Arithmetica

1. Introduction. Let K be a field of characteristic p ≥ 0 and let f(X) be a polynomial of degree at least two with coefficients in K. We set f₁(X) = f(X) and define f r + 1 ( X ) = f ( f r ( X ) ) for all r ≥ 1. Following R. W. K. Odoni [7], we say that f is stable over K if f r ( X ) is irreducible over K for every r ≥ 1. In [6] the same author proved that the polynomial f(X) = X² - X + 1 is stable over ℚ. He wrote in [7] that the proof given there is quite difficult and it would be of interest to have an elementary proof. In the sequel...

Left MQQs whose left parastrophe is also quadratic

Simona Samardjiska, Danilo Gligoroski (2012)

Commentationes Mathematicae Universitatis Carolinae

A left quasigroup ( Q , q ) of order 2 w that can be represented as a vector of Boolean functions of degree 2 is called a left multivariate quadratic quasigroup (LMQQ). For a given LMQQ there exists a left parastrophe operation q ∖ defined by: q ∖ ( u , v ) = w ⇔ q ( u , w ) = v that also defines a left multivariate quasigroup. However, in general, ( Q , q ∖ ) is not quadratic. Even more, representing it in a symbolic form may require exponential time and space. In this work we investigate the problem of finding a subclass of LMQQs whose left parastrophe...

Lifting solutions over Galois rings.

Javier Gómez-Calderón (1990)

Extracta Mathematicae

In this note we generalize some results from finite fields to Galois rings which are finite extensions of the ring Zpm of integers modulo pm where p is a prime and m ≥ 1.

Currently displaying 181 – 200 of 497