Criterion forrth power residuacity

Residuacity of Primes

Let q,p be distinct primes with p — ef + 1. A variant of the Kummer-Dedekind theorem is proved for Gaussian periods, which shows in particular that q is an e-th power (modp) if and only if the Gaussian period polynomial of degree e has e (not necessarily distinct) linear factors (modg). This is applied to give a simple criterion in terms of the parameters in the partitions p = 8 / + 1 = X 2 + Y...

Residuacity and genus theory of forms

Article history: Received 13 November 2009 Revised 15 March 2011 Accepted 7 June 2011 Available online xxxx Communicated by David Goss MSC: primary 11D09, 11A55 secondary 11R11, 11R29

What Criterion for a Power Algorithm?

Quartic residuacity and the quadratic character of certain quadratic irrationalities

We prove a general theorem that evaluates the Legendre symbol (A+B √ m p) under certain conditions on the integers A, B, m and the prime p. The evaluation is in terms of parameters appearing in a binary quadratic form representing p. The theorem has applications to quartic residuacity.

ADAPTIVE FILTERING WITH ADAPTIVE p-POWER ERROR CRITERION

In a previous paper, we have proposed a novel approach to choose an optimal p-power error criterion for adaptive filtering, by minimizing a Kullback-Leibler information divergence (KL-divergence). However, the method requires exact knowledge of the noise PDF, which reduces its practicality since in real life scenario the noise distribution is usually unknown. In the present paper, we propose a ...