Related papers: Remarks on an interpolation between Wilson's theor…

We give the connections among the Fekete sets, the zeros of orthogonal polynomials, $1(w)$-normal point systems, and the nodes of a stable and most economical interpolatory process via the Fej\'er contants. Finally the convergence of a…

We give a new construction of q-Genocchi numbers, Euler numbers of higher order, which are different than the q-Genocchi numbers of Cangul-Ozden-Simsek. By using our q-Genoucchi, Euler nimbers of higher order, we can investigate the…

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

I discuss the computational methods behind the formulation of some conjectures related to variants on Andrews' $q$-Dyson conjecture.

The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.

The `Congruence Conjecture' was developed by the second author in a previous paper. It provides a conjectural explicit reciprocity law for a certain element associated to an abelian extension of a totally real number field whose existence…

This is a survey on Kawaguchi-Silverman conjecture.

One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems and present a couple of applications of them.

By recent work of the author, Wilson's theorem as well as the Wilson quotient can be described by supercongruences of power sums of Fermat quotients modulo every higher prime power. We translate these congruences into congruences of power…

We combine two of Igusa's conjectures with recent semi-continuity results by Musta\c{t}\u{a} and Popa to form a new, natural conjecture about bounds for exponential sums. These bounds have a deceivingly simple and general formulation in…

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

This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…

We study some versions of the statement of Hadwiger's conjecture for finite as well as infinite graphs.

In Wilson's Theorem the primality of a number hinges on a congruence. We present a similar test where the primality of a number m hinges, instead, on the indivisibility of 4(m-5)! by m. One implication of this theorem is a necessary and…

Using Eulerian and Euler numbers, we establish congruences concerning sums involving harmonic numbers, tangent numbers and Genocchi numbers.

In this paper, we give a simple counter example to the famous Hodge conjecture.

We present two related conjectures, arising in work on i-matchings in random r-regular bipartite graphs. The conjectures themselves are easily stated and involve only basic properties of convergent power series. One formulation involves…

In this paper, we prove the conjecture of Yui and Zagier concerning the factorization of the resultants of minimal polynomials of Weber class invariants. The novelty of our approach is to systematically express differences of certain Weber…

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.