Abstract:
The Borwein Conjecture predicts the sign pattern of the coefficients of the polynomial
(1-q)(1-q^2)(1-q^4)(1-q^5) ... (1-q^{3n-2})(1-q^{3n-1}) .
It was posed around 1990 by Peter Borwein and popularised by George Andrews. Several attempts to prove the conjecture have been made over the years, most of them by combinatorial means or by the manipulation of q-series. In the talk, I will present a proof that is based on saddle point approximations of the coefficients of this polynomial.