Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415563 | Journal of Number Theory | 2013 | 25 Pages |
Abstract
In this paper we show that for kâNâª{0}, under natural assumptions on the functions g and h, for a large class of Riemann integrable functions f:[0,1]k+1âR (not all, for kâN; and all, for k=0), the following equality holdslimxââ1h(x)ân⩽xf(nx,ln1nln1x,â¦,lnknlnkx)g(n)=â«01f(x,1,â¦,1︸k-times)dx. Using these results for prime numbers, we obtain some new extensions of the classical version from 1917 Polyaʼs theorem in number theory.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Magdalena BÄnescu, Dumitru Popa,