ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 68,   1   (1999)
pp.   27-35

AN OMEGA THEOREM ON DIFFERENCES OF TWO SQUARES, II
M. KUHLEITNER

Abstract.  Let $\rho(n)$ denote the number of pairs $(u,v)\in \N\times \Z$ with $u^2-v^2=\nomathbreak n$. Due to a formula of Sierpinski, $\rho(n)$ is closely related to the classical divisor function $d(n)$. We establish a lower bound for the remainder term in the asymptotic expansion for the Dirichlet summatory function of $\rho(n)$.

AMS subject classification.  11N37
Keywords.  Divisor problem, Dirichlet summatory function, asymptotic expansion