Published online by Cambridge University Press: 24 October 2008
In discussing Hecke's function
where {t} = t − [t] − ½ Hardy and Littlewood* made use of the identity
Here
θ is an irrational number between 0 and 1, and pν/qν is the νth convergent to θ (beginning with p0 = 0, q0 = 1). The proof of (1) given by Hardy and Littlewood is of an analytic character.
* Hambury Abh. 3 (1923), 57–68.Google Scholar