Christian Axler

activity

20152022

most citedOn a sequence involving the prime numbers

2 citations · 2 across the 7 of their papers we have counts for

collaborators

8 papers

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 $π (x)$ and t…

math.NT2021

On Robin's inequality

Christian Axler

Let $σ (n)$ denotes the sum of divisors function of a positive integer $n$ . Robin proved that the Riemann hypothesis is true if and only if the inequality $σ (n) < e^{γ} n lo g lo g n$ …

math.NT2019

Some Results on a Conjecture of Hardy and Littlewood

Christian Axler

Let $m$ and $n$ be positive integers with $m, n \geq 2$ . The second Hardy-Littlewood conjecture states that the number of primes in the interval $(m, m + n]$ is always less than or equ…

math.NT2017

On the number of primes up to the $n$ th Ramanujan prime

Christian Axler

The $n$ th Ramanujan prime is the smallest positive integer $R_{n}$ such that for all $x \geq R_{n}$ the interval $(x /2, x]$ contains at least $n$ primes. In this paper we undertake a s…

math.NT2017

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 $C_{n} = n p_{n} - \sum_{k \leq n} p_{k}$ , $n \geq 1$ ,…

math.NT2017

Estimates for $π (x)$ for large values of $x$ and Ramanujan's prime counting inequality

Christian Axler

In this paper we use refined approximations for Chebyshev's $ϑ$ -function to establish new explicit estimates for the prime counting function $π (x)$ , which improve the curre…

New estimates for some integrals of functions defined over primes

On Robin's inequality

Some Results on a Conjecture of Hardy and Littlewood

On the number of primes up to the nth Ramanujan prime

Improving the Estimates for a Sequence Involving Prime Numbers

Estimates for π(x) for large values of x and Ramanujan's prime counting inequality

On the number of primes up to the $n$ th Ramanujan prime

Estimates for $π (x)$ for large values of $x$ and Ramanujan's prime counting inequality