相关论文: Notes on the multiplicity conjecture

In this note we provide some results related to the Koethe conjecture and exhibit that the condition R satisfies the Koethe conjecture given in [2, theorem 2.6 ] is superfluous at least under certain conditions described in this note.

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

This paper establishes mixed multiplicity formulas concerning the relationship between mixed multiplicities of modules and mixed multiplicities of rings via rank of modules.

Theoretical and experimental studies of high multiplicity events are analyzed. Some interesting phenomena can be revealed at high multiplicities. Preliminary results of project "Thermalization" are reported.

We prove the multiplicity one case of Lusztig's conjecture on the irreducible characters of reductive algebraic groups for all fields with characteristic above the Coxeter number.

We make a summary of the different types of proofs adding some new ideas. In addition we conjecture some relations which could be necessary in "modular type proofs" (not still found) of the Ramanujan-like series for 1/\pi^2.

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

A new kind of diagrams is presented, showing the causal structure of bimetric interactions.

In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…

In this short note we apply a recent theorem of Koll\'ar about the arithmetic genus of curves to give a bound on the number of joints weighted by the multiplicities. This gives an affirmative answer to a conjecture of Carbery in the generic…

These are notes from a basic course in Several Complex Variables

General considerations on the Equivalence conjectures and a review of few mathematical results.

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

We describe recent advances in the study of random analogues of combinatorial theorems.

In this paper, we state a conjecture on the prime factorization of numbers of the form $n!+1$, explore its implications, and compare it with empirical evidence and established results based on the $abc$ conjecture.

Let $p$ be an odd prime. In the paper we collect the author's various conjectures on congruences modulo $p$ or $p^2$, which are concerned with sums of binomial coefficients, Lucas sequences, power residues and special binary quadratic…

We extend a conjecture of Kimberley-Robertson on the abelianizations of certain square complex groups.

A variation on the splitting principle

A few remarks on hep-ph/9612213 are given.