Related papers: On Ryser's Conjecture
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We give a new simpler proof of a theorem of Jayne and Rogers.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
This paper is a continuation of Arai's paper on derivability conditions for Rosser provability predicates. We investigate the limitations of the second incompleteness theorem by constructing three different Rosser provability predicates…
We obtain some results related to Romanoff's theorem.
In this paper, we prove a conjecture of Schnell in the surface case.
In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient…
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…
This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…
We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.
We obtain some new inequalities of Chebyshev Type.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
We give a counterexample to a recently conjectured variant of the Penrose inequality.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.
We present a question which implies a complete positive answer for the Bass-Quillen Conjecture.
We show that the Jacobian conjecture of the two dimensional case is true.
We prove a central limit theorem with aassumptions which are many weak than classical conditions
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
A proof of Sendov's conjecture is given.