Triple correlation sums of coefficients of θ-series

Abstract

We investigate the triple correlation sums of coefficients of $ \theta $-series and prove an asymptotic formula with power-saving error term. As a result, we present that this type of sum is non-trivial in the regime $ H\ge X^{2/3+\varepsilon} $.

Keywords

• jacobi theta series
• fourier coefficients
• triple correlation sums
• asymptotic formula