English

Formules pour les nombres premiers

Number Theory 2007-05-23 v1
Authors: A. Balan
View on arXiv ↗ PDF ↗

Abstract

The distribution of prime numbers is here considered. We show a formula for li−1li^{-1} and we study the π(x)\pi(x) function and Riemann's hypothesis.

Keywords

prime numbers pi computation prime number theory

Cite

@article{arxiv.math/0105003,
  title  = {Formules pour les nombres premiers},
  author = {A. Balan},
  journal= {arXiv preprint arXiv:math/0105003},
  year   = {2007}
}

Comments

In french

Related papers

View all related →
Number Theory · Mathematics
On Statistics of the Riemann Zeros Differences
Yuri Bachilov
2014-02-06
Number Theory · Mathematics
On the random nature of (prime) number distribution
Erika Alvarez, Jean Pestieau
2007-05-23
Number Theory · Mathematics
Improving riemann prime counting
Michel Planat, Patrick Solé
2017-04-12
Classical Analysis and ODEs · Mathematics
Riemann hypothesis and some new integrals connected with the integral negativity of the remainder in the formula for the prime-counting function $\pi(x)$
Jan Moser
2011-05-26
Number Theory · Mathematics
The prime number theorem for primes in arithmetic progressions at large values
Ethan S. Lee
2023-03-10
Mathematical Physics · Physics
Prime Number Diffeomorphisms, Diophantine Equations and the Riemann Hypothesis
Lubomir Alexandrov, Lachezar Georgiev
2007-05-23
General Mathematics · Mathematics
An algorithm for the prime-counting function of primes larger than three
Yuri Heymann
2020-03-24
General Mathematics · Mathematics
An Exact Formula for the Prime Counting Function
Jose Risomar Sousa
2021-04-02
Number Theory · Mathematics
New bounds for the prime counting function \pi(x)
Christian Axler
2016-01-13
Number Theory · Mathematics
A computational history of prime numbers and Riemann zeros
Pieter Moree, Izabela Petrykiewicz, Alisa Sedunova
2018-10-15
General Mathematics · Mathematics
Defining the prime numbers prior to the integers: A first-principles approach to the distribution of primes
Kolbjørn Tunstrøm
2018-08-30
Number Theory · Mathematics
Several new relations for the $n^{th}$ prime number
Boris B. Benyaminov
2011-08-16
Number Theory · Mathematics
A Direct Proof of the Prime Number Theorem using Riemann's Prime-counting Function
Zihao Liu
2022-07-13
Number Theory · Mathematics
New estimates for some integrals of functions defined over primes
Christian Axler
2022-03-18
Number Theory · Mathematics
Distribution law for twin primes amongst naturals
Boris B. Benyaminov
2011-08-02
Number Theory · Mathematics
Improving bounds on prime counting functions by partial verification of the Riemann hypothesis
Daniel R. Johnston
2022-06-15
Number Theory · Mathematics
On formula to compute primes and the nth prime
Issam Kaddoura, Samih Abdul-Nabi
2012-04-19
Number Theory · Mathematics
The distribution of primes and Euler characreristic
Kazunori Noguchi
2017-11-09
General Mathematics · Mathematics
Algorithm, probability, and prime numbers
Yasuo Nishii
2026-01-12
Number Theory · Mathematics
Regular and oscillatory parts for basic functions of prime numbers. I Regular parts
R. M. Abrarov, S. M. Abrarov
2007-05-23
Number Theory · Mathematics
A Prime Number Theorem for Rankin-Selberg L-functions over Number fields
Tim Gillespie, Guanghua Ji
2009-10-20
General Mathematics · Mathematics
An explicit formula for Pi(x) in the form of a sum over the Non-trivial zeros of the Riemann Zeta function
Jose Javier Garcia Moreta
2007-05-23
Number Theory · Mathematics
On the logarithm of the Riemann zeta-function and its iterated integrals
Shōta Inoue
2019-12-11
General Mathematics · Mathematics
Analytic implications from the remainder term of the prime number theorem
Yuan-You Fu-Rui Cheng
2010-07-27
Classical Analysis and ODEs · Mathematics
Riemann hypothesis and some new asymptotically multiplicative integrals which contain the remainder of the prime-counting function $\pi(x)$
Jan Moser
2010-11-03