We find explicit models for the PSL2(C)and SL2(C)-character varieties of the fundamental groups of complements in S of an infinite family of two-bridge knots that contains the twist knots. We compute… (More)

The classical theorem of Bombieri and Vinogradov is generalized to a non-abelian, non-Galois setting. This leads to a prime number theorem of “mixed-type” for arithmetic progressions “twisted” by… (More)

Let K be a number field with unit rank at least four, containing a subfield M such that K/M is Galois of degree at least four. We show that the ring of integers of K is a Euclidean domain if and only… (More)

We investigate a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if its set of… (More)

Let K be a number field with positive unit rank, and let OK denote the ring of integers of K. A generalization of Artin’s primitive root conjecture is that that OK is a primitive root set for… (More)

We determine the PSL2(C) and SL2(C) character varieties of the once-punctured torus bundles with tunnel number one, i.e. the once-punctured torus bundles that arise from filling one boundary… (More)

Let K be a number field with r real places and s complex places, and let OK be the ring of integers of K. The quotient [H]×[H]/PSL2(OK) has hK cusps, where hK is the class number of K. We show that… (More)

The J(k, l) knots, often called the double twist knots, are a subclass of two-bridge knots which contains the twist knots. We show that the A-polynomial of these knots can be determined by an… (More)

BACKGROUND
Posterior urethral valves (PUV) are a common cause of congenital obstructive nephropathy. The outcome of patients with PUV at Chris Hani Baragwanath Academic Hospital in Johannesburg,… (More)