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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.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…