Related papers: On a conjecture by Y. Last
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We show that $\lambda$-symmetries can be algorithmically obtained by using the Jacobi last multiplier. Several examples are provided.
We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.
We show that the Jacobian conjecture of the two dimensional case is true.
In this paper, using some arithmetic properties of Jacobi sums, we investigate some products involving Jacobi sums and reveal the connections between these products and certain cyclotomic matrices. In particular, as an application of our…
We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.
We prove the Strong Jacobi Bound Conjecture for generically reduced components of differential schemes.
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.
We obtain a finite form of Jacobi's identity and present a combinatorial proof based on the structure of synchronized partitions.
The point of this note is to prove that the secrecy function attains its maximum at y=1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Sol\'e. Further, we will give a very simple…
We prove a sharp Lieb-Thirring type inequality for Jacobi matrices, thereby settling a conjecture of Hundertmark and Simon. An interesting feature of the proof is that it employs a technique originally used by Hundertmark-Laptev-Weidl…
We prove a recent conjecture by Ulas on reducible polynomial substitutions.
The said paper [2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is with gaps.
Let S be a polynomial ring over a field of characteristic zero in finitely may variables. Let T be an unramified, finitely generated extension of S with $T^\times = k^\times$. Then T = S.
In this paper we prove the WALA conjecture.
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 prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).
We survey recent developments on the Restriction conjecture.
A particular case of the Jacobian conjecture is considered and for small dimensional cases a computational approach is offered
The article provides a counterexample to a conjecture by Blocki-Zwonek.