Related papers: Notes on the multiplicity conjecture

Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

Work in progress concerning alternative formalizations of arithmetic.

We survey the classical results on the prime number theorem

An observation on Hall-Littlewood polynomials.

This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

An overview of the recent developments in plurifine potential theory.

We present some new lower bound estimates for certain numbers in Laver table theory and introduce several related structures of interest.

In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

In this paper, we give a survey of the recent develpoments of the DDVV conjecture.

We introduce a new conjecture on products of two distinct primes that would provide a partial answer to a conjecture of McIntosh. Also, $\binom{2p-1}{p-1}-1$ is written in terms of a polynomial in prime $p$ over the integers and we discuss…

We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.

We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

Using Singular Rescaling We Prove Some Bifurcation Results. This note Presents short proofs for some Bifurcation results which had been appeared with other authors.