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math.NT2022
On Ramanujan's prime counting inequality
Christian Axler
In this paper, we give a new upper bound for the number which is defined to be the smallest positive integer such that a certain inequality due to Ramanujan invol…
math.NT2022
New estimates for some integrals of functions defined over primes
Christian Axler
In this paper we give new estimates for integrals involving some arithmetic functions defined over prime numbers. The main focus here is on the prime counting function and t…
math.NT2022
Effective estimates for some functions defined over primes
Christian Axler
In this paper we give effective estimates for some classical arithmetic functions defined over prime numbers. First we find the smallest real number so that some inequality i…