Related papers: Nonrationality of a generic cubic fourfold
This paper has been withdrawn by the authors due to some fatal errors in the analysis.
withdrawed due to a substantial error.
This paper has been withdrawn by the author, due to an error in relation (11).
Paper withdrawn. There is a gap in the proof of Proposition 4.3 (its conclusion ``d'o\`{u} la proposition.'' is incorrect). Therefore theorems 1.1 and 3.1, which were the main results of the paper, are not proved.
This paper presents geometric proofs for the irrationality of square roots of select integers, extending classical approaches. Building on known geometric methods for proving the irrationality of sqrt(2), the authors explore whether similar…
The paper was withdrawn due to a gap in the proof of Lemma 3.
This paper has been withdrawn as the statements in Proposition 4.4 and Theorem 1.4(i) are not correct.
The manuscript has been withdrawn because it has a fatal flaw caused by a misinterpretation of the Copeland-Erdos theorem.
We compute the dynamical degrees of certain compositions of reflections in points on a smooth cubic fourfold. Our interest in these computations stems from the irrationality problem for cubic fourfolds. Namely, we hope that they will…
We employ the second order of the derivative expansion of the nonperturbative renormalization group to study cubic ($\mathbb{Z}_4$-symmetric) perturbations to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide…
This paper has been withdrawn by the author due to a crucial sign error in equation 1
We study the existence of a Chow-theoretic decomposition of the diagonal of a smooth cubic hypersurface, or equivalently, the universal triviality of its ${\rm CH}_0$-group. We prove that for odd dimensional cubic hypersurfaces or for cubic…
The paper has been withdrawn by the author due an error in the proof of Theorem 3.2.
We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers a so that either (a, a^2) or (a,…
We present an analytic derivation of the full four-loop cusp anomalous dimension of $\mathcal{N}=4$ supersymmetric Yang-Mills theory from the Sudakov form factor. To extract the cusp anomalous dimension, we calculate the $\epsilon^{-2}$…
This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.
This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.
The original versions (1 and 2) of this paper paper contain a fatal error. All my attempts to patch the error have failed. As a service to the community I explain the error in some detail.
This paper has been withdrawn due to an error in the proof of the main theorem.
We show that the Lambert series $f(x)=\sum d(n) x^n$ is irrational at $x=1/b$ for negative integers $b < -1$ using an elementary proof that finishes an incomplete proof of Erdos.