Related papers: Some discussions on the Goldbach conjecture

The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer $n$ greater than $5$ is the sum of three primes. The present paper proves this conjecture. Both the ternary Goldbach conjecture and the binary, or…

We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.

We present an overview of bounds on zeros of $L$-functions and obtain some improvements under weak conjectures related to the Goldbach problem.

We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.

The Hodge conjecture is shown to be equivalent to a question about the homology of very ample divisors with ordinary double point singularities. The infinitesimal version of the result is also discussed.

It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture, constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.

We give a more comrehensive treatment of Chen's double sieve and improve related constants in Goldbach's conjecture and the twin prime problem.

We describe some open questions related to support points in the class $S^0$ and introduce some useful techniques toward a higher dimensional Bieberbach conjecture.

First a few reformulations of Frankl's conjecture are given, in terms of reduced families or matrices, or analogously in terms of lattices. These lead naturally to a stronger conjecture with a neat formulation which might be easier to…

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

Goldbach's comet is the plot of the Goldbach function g(n), in the interval [3, N], with a large positive integer N. The function g(n) counts the number of different ways in which 2n can be expressed as the sum of two odd primes. An…

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…

Grothendieck's standard conjecture of Lefschetz type has two main forms: the weak form $C$ and the strong form $B$. The weak form is known for varieties over finite fields as a consequence of the proof of the Weil conjectures. This suggests…

The grouplike elements of a coalgebra over a field are known to be linearly independent over said field. Here we prove three variants of this result. One is a generalization to coalgebras over a commutative ring (in which case the linear…

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

We investigate progressions in the set of pairs of integers $\mathbb{Z}^2$ and define a generalisation of the Jacobsthal function. For this function, we conjecture a specific upper bound and prove that this bound would be a sufficient…

New cases of the multiplicity conjecture are considered.

We present a selection of known as well as new variants of the Sensitivity Conjecture and point out some weaker versions that are also open.

In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.