Related papers: Collatz Problem of Positive Integers

This paper has been withdrawn by the author.

This paper has been withdrawn by the author, due to the insecurity against attacks received in quant-ph/0605027v5.

This paper has been withdrawn by the author

This document is withdrawn due to an error in Lemma 4.

This paper has been withdrawn by the authors, due to a possible flaw in its logic. Namely, it has been taken for granted that the the structure of regular part of Helmholtz free energy is insensitive to the sign of the specific heat…

This paper has been withdrawn by the author.

This paper has been withdrawn. See v1 still available to understand the problem: Proposition 2.2 is false. The error in the proof is in claim (3). Then, the whole paper collapses. We do not have any correction for now. We apologize to…

This paper has been withdrawn by the author.

This paper was withdrawn by the author due to a fatal error.

This paper has been withdrawn by the author as it has already been submitted under the title "Twisted character of a small Representation of GL(4)".

This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.

This article has been withdrawn.

This paper has been withdrawn by the author due to a crucial sign error in equation 1

This paper has been withdrawn by the author, due to errors in the figures.

This paper has been withdrawn by the author, due to necessity of revision.

This paper has been withdrawn

This paper has been withdrawn by the author, since the author does not have enough time to answer every questions on this result.

This paper has been withdrawn by the author due to an error in equations 39 and 41.

This submission has been withdrawn at the request of the author.

This paper has been withdrawn while the author verifies the literature.