11 citations · 23 across the 17 of their papers we have counts for
5 papers · 1 filter
On the number of primes up to the th Ramanujan prime
Christian Axler
The th Ramanujan prime is the smallest positive integer such that for all the interval contains at least primes. In this paper we undertake a s…
Improving the Estimates for a Sequence Involving Prime Numbers
Christian Axler
Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence , ,…
New estimates for the th prime number
Christian Axler
In this paper we establish a new explicit upper and lower bound for the -th prime number, which improve the currently best estimates given by Dusart in 2010. As the main tool we…
Estimates for for large values of and Ramanujan's prime counting inequality
Christian Axler
In this paper we use refined approximations for Chebyshev's -function to establish new explicit estimates for the prime counting function , which improve the curre…
New estimates for some functions defined over primes
Christian Axler
In this paper we first establish new explicit estimates for Chebyshev's -function. Applying these new estimates, we derive new upper and lower bounds for some functions…