Related papers: Counterexamples to the pseudo-Riemannian Lichnerow…
This paper has been withdrawn by the author due to an erro thereon line -2 of page 4.
We contribute to the lively debate in current scholarship on the Leibnizian calculus. In a recent text, Arthur and Rabouin argue that non-Archimedean continua are incompatible with Leibniz's concepts of number, quantity and magnitude. They…
The Shapiro conjecture in the real Schubert calculus, while likely true for Grassmannians, fails to hold for flag manifolds, but in a very interesting way. We give a refinement of the Shapiro conjecture for the flag manifold and present…
They are possible other cases at first done not contemplate. This paper has been withdrawn by the author due to a crucial sign error in equation 1 page 4
We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…
This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas
This paper have serious error in the proof of main theorem 1.1.Result is not proved.
withdrawed due to a substantial error.
We provide a generalization of the Phragm\'en-Lindel\"of principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in the literature.
In this note, we give item-by-item responses to the criticisms raised in [TZ] by Tehrani ad Zinger on our paper [LR]. We illuminate the main ideas and contributions in [LR] in section 2, itemize the responses to issues raised in [TZ] and…
This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.
The proof of the inequalities for alternating Mathieu type series in Journal of Mathematical Inequalities (2008) by \v{Z}. Tomovski and R. Hilfer contains a mistake. Here we give the values of parameters for which these inequalities are not…
The second author studied arithmetic properties of a class of sequences that generalize the sequence of derangements. The aim of the following paper is to disprove two conjectures stated in \cite{miska}. The first conjecture regards the set…
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
In the article [PR1] {\it On Hrushovski's proof of the Manin-Mumford conjecture} (Proceedings of the ICM 2002), R. Pink and the author gave a short proof of the Manin-Mumford conjecture, which was inspired by an earlier model-theoretic…
Boris Shoikhet noticed that the proof of lemma 1 in section 2.3 of math.QA/0504420 contains an error. In this note I give a correct proof of this lemma which was suggested to me by Dmitry Tamarkin. The correction does not change the results…
In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.
In this paper we propose and prove an anticyclotomic Iwasawa main conjecture for Heegner points on supersingular elliptic curves with $a_p=0$. The result has a "$\pm$" nature in the sense of Kobayashi. The proof uses a recent work of the…
Let $\lambda$, $\mu$, $\lambda'$, $\mu'$ be partitions. The conjecture of Lam, Postnikov and Pylyavskyy states that, if $\lambda+\mu = \lambda' + \mu'$, and $\min(\lambda_i-\lambda_j, \mu_i-\mu_j) \leq \lambda'_i - \lambda'_j \leq…
The Legendre conjecture has resisted analysis over a century, even under assumption of the Riemann Hypothesis. We present, a significant improvement on previous results by greatly reducing the assumption to a more modest statement called…