Related papers: Further Improvements on Waring's Problem

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.

This paper is devoted to a discussion of specific properties of invariants in the theory of forms.

A possible method to solve the sign problem is developed by modifying the original theory. Considering several modifications of the partition function, the observable in the original theory is reconstructed from the identity connecting the…

We describe mean value estimates for exponential sums of degree exceeding 2 that approach those conjectured to be best possible. The vehicle for this recent progress is the efficient congruencing method, which iteratively exploits the…

The invariant subspace problem is solved correcting my earlier attempts [6]-[12].

This paper is the extended introduction of a serie of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other…

We provide some new results of the ground state of quantum layers.

I give a brief overview of fault-tolerant quantum computation, with an emphasis on recent work and open questions.

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.

This paper is a continuation of our recent work in [9].

We discuss recent progress in understanding the issues essential to the development of better cone jet algorithms.

This note is developing, and we will include many additions in the near future. Our purpose here is to highlight that there is plenty of space for a topological development of the Fermat Real Line.

In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases.

In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.

In this paper we survey many of the known results about Morse boundaries and stability.

The Waring problem of forms concerns the expression of homogeneous multivariate polynomials as sums of powers of linear forms. This paper focuses on complex binary forms, and we solve the Waring problem for them using basic tools in algebra…

This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future…

The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.

Eq.(19) is added and related issues are further clarified. Also some typos and signs a re corrected.

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.