Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11012890 | Journal of Number Theory | 2019 | 7 Pages |
Abstract
We study the series s(n,âx) which is the sum for k from 1 to n of the square of the sine of the product x Gamma(k)/k, where x is a variable. By Wilson's theorem we show that the integer part of s(n,âx) for x = Pi/2 is the number of primes less or equal to n and we get a similar formula for x a rational multiple of Pi. We show that for almost all x in the Lebesgue measure s(n,âx) is equivalent to n/2 when n tends to infinity, while for almost all x in the Baire sense, 1/2 is a limit point of the ratio of s(n,âx) to the number of primes less or equal to n.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alain Connes,