3 papers
math.NT2006
Irreducible polynomials in F_q[x] versus 1 - qz in C[z]
Barry Brent
Let q be a prime power and N_n count degree-n monic irreducible polynomials in F_q[x]. We show that prod_{n=1}^{\infty} (1 -z^n)^N_n = 1 - qz for small |z|.
math.DS2002
3x+1 dynamics on rationals with fixed denominator
Barry Brent
We propose the existence of an infinite class of exact analogues of the 3x+1 conjecture for rational numbers with fixed denominators. For some other denominators, there are several…
math.NT1998
Quadratic minima and modular forms
Barry Brent
We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for Γ_0(2). Numerical evid…