Email : a l e x . b a l i @ s f r . f r
But I must admit, I never actually use it
If you wanna contact me, use either Messenger...
( h t t p : / / w w w . f a c e b o o k . c o m /
A l e x H D P l a y i n g )
... or my Discord : @ b e r l i n g o t d e l a i t # 9 7 6 5
I'm interested in everything that is closely linked to
mathematics, in any field of study. Whatever I do, I
publish it here. The fields in which I'm more proficient
are currently number theory and analysis, but I wish to
get into group theory and algebraic topology as soon as
Papers and drafts :
Various patterns and anomalous behaviors from the sine function
(Scribd, 30 Oct 2018)
Weak evidence for Goldbach's conjecture
(Scribd, 20 Oct 2018)
In this paper, we will present a bunch of sets which tend to reveal somewhat strange patterns from the sine function, and we'll specifically study those who don't really fit in any of those.
On the eventuality of a smallest countexample of the Collatz conjecture
(Scribd, 29 Sep 2018)
In this tiny paper, we will show our recent work on Goldbach's conjecture, which is about whether (or not) all the even numbers greater than or equal to 4 can be equated to a sum of two primes. We will try provide a few weak evidence for the conjecture. We'll conclude on a suggestion to prove Goldbach or the weaker conjecture that asks if infinitely many even numbers can be written as a sum of two primes.
A draft on the repartition of algebraic numbers
(Scribd, 02 Jul 2018)
In this paper, we will show a few results which would be implied if there is indeed a minimal counterexample of the Collatz conjecture, and trying to find out what kind of properties such a number would (or wouldn't) have. We'll also conclude with an idea to find a better algorithm, which we unfortunately had a hard time to decipher.
A lot of unsolved number theoretic open problems are about the irrationality or the transcendence of a number. This paper will share a few results which
are useful to know about the repartition of algebraic numbers. We will specifically look at quadratic roots as quadratics are easier to study than most
other polynomials, and because they also contain ℂ\ℝ roots.