Related papers: Linearizability of cubic polynomials at irrational…

H. Lenstra has pointed out that a cubic polynomial of the form (x-a)(x-b)(x-c) + r(x-d)(x-e), where {a,b,c,d,e} is some permutation of {0,1,2,3,4}, is irreducible modulo 5 because every possible linear factor divides one summand but not the…

This paper has been withdrawn by the authors, because of a crucial gap in the proof of the main theorem.

The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper has been withdrawn by the author due to a crucial error in the formulation.

Following earlier results of Sondow, we propose another criterion of irrationality for Euler's constant $\gamma$. It involves similar linear combinations of logarithm numbers $L\_{n,m}$. To prove that $\gamma$ is irrational, it suffices to…

This paper has been withdrawn due to a critical error discovered in Theorem 4.21. Anyone with a historical or pragamatic interest in prior "negative results", however - e.g., failed proof attempts relating to the (in)consistency of ZF or…

This paper has been withdrawn by the author due to that the main results and approaches are closedly parallel to the ones in Lie algebra case.

This paper has been withdrawn by the author, due to possible counter-examples.

This paper has been withdrawn by the author due to a error in attachment of source file.

This paper has been withdrawn by the authors because it has been combined with "Higher Auslander Algebras Admitting Trivial Maximal Orthogonal Subcategories" (arXiv:0903.0761) together. Please see the new version of the latter paper for the…

This paper has been withdrawn by the author(s), due a crucial i-number error in Eqn. 18.

A. Mukhopadhyay, M. R. Murty and K. Srinivas (http://arxiv.org/abs/0808.0418) have recently studied various arithmetic properties of the discriminant $\Delta_n(a,b)$ of the trinomial $f_{n,a,b}(t) = t^n + at + b$, where $n \ge 5$ is a fixed…

This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.

This paper has been withdrawn by the author due to serious error found in main argument.

This paper has been withdraw by the authors. An enlarged and complete analysis of the constraints is presented in hep-th/9910163. It includes also relativistic particles and strings. The non-relativistic particle quantization has been…

The paper is withdrawn.

This paper has been withdrawn because the result turns out to be trivial.

This paper is withdrawn. The current main theorem can be proved by using a simple field theory. The main theorem is to placed by another theorem, shortly.

This paper has been withdrawn by the author due to a crucial error in equation.

This paper has been withdrawn by the author due to a crucial error.