Glasnik matematički, Vol. 53 No. 1, 2018.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.53.1.01
New upper bounds for Ramanujan primes
Anitha Srinivasan
; Saint Louis University - Madrid Campus, Avenida del Valle 34, 28003 Madrid, Spain
Pablo Ares-Gastesi
; Department of Applied Mathematics and Statistics, School of Business and Economics, Universidad CEU San Pablo, Madrid, Spain
Sažetak
For n≥ 1, the nth Ramanujan prime is defined as the smallest positive integer Rn such that for all x≥ Rn, the interval (x/2, x] has at least n primes. We show that for every ε>0, there is a positive integer N such that if α=2n(1+(log 2+ε)/(log n+j(n))), then Rn< p[α] for all n>N, where pi is the ith prime and j(n)>0 is any function that satisfies j(n)→ ∞ and nj'(n)→ 0.
Ključne riječi
Ramanujan primes; upper bounds
Hrčak ID:
201806
URI
Datum izdavanja:
20.6.2018.
Posjeta: 846 *