On the Fourier coefficients of small positive powers of \(\theta\) (\(\tau\) ) (Q1078597)

The main result of the paper is : \(r_ s(n)=\rho_ s(n)\) for \(8/3<s<4\), where \(r_ s(n)\) is defined by \(\theta^ s(\tau)=1+\sum^{\infty}_{n=1}r_ s(n)\quad e^{\pi in\tau}\) and \(\rho_ s(n)\) is the singular series. The proof uses techniques introduced by Maass and relies upon recent results of Goldfeld and Sarnak on Selberg's Kloosterman zeta-function.