Related papers: A note on the Hodge conjecture

In this note I give an information-theoretic proof of the Bonami-Beckner-Gross hypercontractive inequality.

We discuss Hodge-theoretic aspects, related to the loop Grassmannian, of the strong Macdonald conjecture (whose proof is joint work with Fishel and Grojnowski).

We present a theorem about irreducibility of a polynomial that is the resultant of two others polynomials. The proof of this fact is based on the field theory. We also consider the converse theorem and some examples.

We improve constants in the Rademacher-Menchov inequality.

A counterexample is given to the uniqueness result given in the paper by J.Cox and K.Thompson, "Note on the uniqueness of the solution of an equation of interest in inverse scattering problem", J. Math.Phys., 11, N3, (1970), 815-817.

A family of congruences interpolating between those of Wilson and Giuga is constructed. Several elementary results are established, in order to present a possible approach to establishing Giuga's conjecture.

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.

Alternative approaches to Lebesgue integration are considered.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.

The aim of this note is to prove the analogue of Poincar\'e duality in the chiral Hodge cohomology.

This is a short note on the log canonical inversion of adjunction.

This note describes a way of obtaining e that differs from the standard one. It could be used as an alternate way of showing how the value of e is obtained. No attempt is made to show the existence of the limit in the definition of e that…

In this addendum to [4], we provide a pair of counterexamples relevant to the theory of implicit operations. More precisely, we exhibit a pp expansion of a variety that fails to be a variety (although it is a quasivariety). Furthermore, we…

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

Either fibered knots supporting the tight contact structure are unique in their smooth concordance class or there exists a fibered counterexample to the Slice-Ribbon Conjecture.

We provide a counterexample to P.~Olver's freeness conjecture for $C^\omega$ transformations.

We prove in this paper the Ax-Schanuel conjecture for all admissible variations of mixed Hodge structures.

The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].