相关论文: Notes on the multiplicity conjecture

These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.

This note generalizes factorization for formulas with multiplicities and conjectures that the connection method along with this feature is computationally as powerful as resolution, also seen from a complexity point of view.

In this paper we present many congruences for several Ap\'ery-like sequences.

In this note, we find a new way to prove several properties of 2-alternating capacities.

We present a conjecture on multiplicity of irreducible representations of a subgroup $H$ contained in the irreducible representations of a group $G$, with $G$ and $H$ having the same derived groups. We point out some consequences of the…

We develop a theory of modulus triples, for future motivic applications.

We introduce a new method in the attempt to prove the Jacobian conjecture. In the complex dimension 2 case, we apply this method to prove some new results related the Jacobian conjecture.

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…

Remarks on mathematical proof and the practice of mathematics.

Probably we have observed a new simple phenomena dealing with approximations to two real numbers.

We obtain simple proofs of certain inequalites for bivariate means.

We prove three conjectures, related to the paperfolding sequence, in a recent paper [arXiv:2005.04066] of P. Barry.

In this note I provide two extensions of a particular case of the classical Poncelet theorem.

An technically interesting proof of a known theorem.

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.

Theory of $n$-complements with applications is presented.

Several open problems in algebraic logic are solved.

In this short note we present a family of counterexamples to the King's conjecture.

Following an idea due to Euler, we evaluate the alternating sums of powers of consrcutive integers.

We prove several extensions of the Erdos-Fuchs theorem.