Sign-patterns of Certain Infinite Products

Abstract: The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for the coefficient sign patterns for [ \frac{(q^i;q^i){\infty}}{(q^p;q^p){\infty}} ] for integers ( i > 1 ) and primes ( p > 3 ). The sign analysis for this quotient addresses and extends a conjecture of Bringmann et al. for the coefficients of ( (q^2;q^2){\infty}(q^5;q^5){\infty}^{-1} ). The sign distribution for additional classes of eta quotients is considered. This addresses multiple conjectures posed by Bringmann et al.