This result still holds when k depends on x, limx > ook =
The proofs of the first theorem and the right hand inequality of the second theorem are elementary and presented in a series of six short lemmata. The left hand inequality of the second theorem is proved by an application of a lower bound form of the Selberg sieve.
Classif.: * 11N37 Asymptotic results on arithmetic functions
11A25 Arithmetic functions, etc.
Keywords: divisor function; short intervals; Selberg sieve
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