The general divisor problem

The Circle and Divisor Problem

Generalizing the Titchmarsh Divisor Problem

Let a be a natural number different from 0. In 1963, Linnik proved the following unconditional result about the Titchmarsh divisor problem ∑ p≤x d(p− a) = cx + O ( x log log x log x ) where c is a constant dependent on a. Titchmarsh proved the above result assuming GRH for Dirichlet L-functions in 1931. We establish the following asymptotic relation: ∑ p≤x p≡a mod k d ( p− a k ) = Ckx + O ( x l...

Generalized divisor problem

In 1952 H.E. Richert by means of the theory of Exponents Pairs (developed by J.G. van der Korput and E. Phillips ) improved the above O-term ( see [8] or [4] pag. 221 ). In 1969 E. Krätzel studied the three-dimensional problem. Besides, M.Vogts (1981) and A. Ivić (1981) got some interesting results which generalize the work of P.G. Schmidt of 1968. In 1987 A.Ivić obtained Ω-results for ∫ T 1 ∆ ...

The divisor problem for binary cubic forms

We investigate the average order of the divisor function at values of binary cubic forms that are reducible over Q and discuss some applications. Mathematics Subject Classification (2000). 11N37 (11D25).

On Dirichlet ' S Divisor Problem

tact, whereas those for a = 0.02 imply only 25% more frequent contacts than the all-ornone hypothesis but with rather high though rapidly diminishing attack rates. 10 Schuman and Doull, Amer. Jour. Pub. Health, 30, Supplement to March, 1940, p. 21, state: "From these estimates of carrier prevalence and froni the average annual increment in Shick-negatives, an estimate may be made of the number ...