For the Estermann function is defined as if and by meromorphic continuation otherwise. For prime, we compute the moments of at the central point , when averaging over .
As a consequence we deduce the asymptotic for the iterated moment of Dirichlet -functions , obtaining a power saving error term.
Also, we compute the moments of certain functions defined in terms of continued fractions. For example, writing where is the continued fraction expansion of we prove that for and primes one has as .
"High moments of the Estermann function." Algebra Number Theory 13 (2) 251 - 300, 2019. https://doi.org/10.2140/ant.2019.13.251