A Fourier analysis approach to disprove the weak Shanks conjecture

Jeffrey S. Geronimo, Hugo J. Woerdeman

We derive formulas for the Fourier coefficients of $|f{|}^2$, where $f(z_1,z_2)=(1-\frac{z_1+z_2}{r}{)}^{-\hat{I}\pm }$, in terms of hypergeometric functions. Using these formulas we provide ad…