Related papers: A proof of the Graham Sloane conjecture
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We survey the classical results on the prime number theorem
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.
An abstract version of Galvin's lemma is proven, within the framework of the theory of Ramsey spaces. Some instances of it are explored.
This is an exposition of Gauss's proof of Descartes's rule of signs.
In this paper, we prove the Farrell-Jones Conjecture for the solvable Baumslag-Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
In this note a far extension of the Banach fixed point theorem is proved.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We give a short proof of the strong law of large numbers based on duality for random walk
We give a simple combinatorial proof of the $\lambda_g$ conjectue in genus 2. We use a description of the class $\lambda_2$ as a linear combination of boundary strata, and show the conjecture follows inductively from applications of the…
We establish the exact overlaps conjecture for iterated functions systems on the real line with algebraic contractions and arbitrary translations.
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
We resolve Stillman's conjecture for families of polynomial rings that are graded by any semigroup under mild conditions. Conversely, we show that these conditions are necessary for the existence of a Stillman bound. This has applications…
We prove Okounkov's conjecture, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity and give several more general statements using a recent result of Rhoades and Skandera. An…
We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.
We establish a simple identity and using it we find a new proof of a result of Kloosterman.
In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.
We give positive answer to two conjectures posed by M. E. H Ismail in his monograph [Classical and quantum orthogonal polynomials in one variable, Cambridge University Press, 2005].