Related papers: A counterexample of two Romanov type conjectures
Normalization fails in type theory with an impredicative universe of propositions and a proof-irrelevant propositional equality. The counterexample to normalization is adapted from Girard's counterexample against normalization of System F…
The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.
We show that there is a contradiction between the Riemann's Hypothesis and some form of the theorem on the universality of the zeta function.
We prove a variation of Gronwall's lemma.
We point out that a concise proof of Theorem 2 in the article, 'On a quadratic estimate of Shafer' by L. Zhu contains a small mistake. Correcting this mistake and giving alternative proofs of Theorem 2 is the main aim of this note.
Hypothesis of Riemann is rejected by definition, because {\zeta}(s), where s zeros of {\zeta}(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/2 holds only for the zeros of {\zeta}(s) = 0 and…
We derive a family of $L^p$ estimates of the X-Ray transform of positive measures in $\mathbb R^d$, which we use to construct a $\log R$-loss counterexample to the Mizohata-Takeuchi conjecture for every $C^2$ hypersurface in $\mathbb R^d$…
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
This paper has been withdrawn by author due to an error in the proof.
The group of piecewise projective homeomorphisms of the line provides straightforward counter-examples to the so-called von Neumann conjecture. The examples are so simple that many additional properties can be established.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. We also state and prove a uniqueness property for not necessarily smooth affine…
A counterexample is given for the Knaster-like conjecture of Makeev for functions on $S^2$. Some particular cases of another conjecture of Makeev, on inscribing a quadrangle into a smooth simple closed curve, are solved positively.
We construct a simple acyclic directed graph for which the Bunkbed Conjecture is false, thereby resolving conjectures posed by Leander and by Hollom.
Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this note, we exhibit explicit examples contradicting the full conjecture as it currently…
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the counterexample to Mordell's Pellian Equation Conjecture that can…
This is a Bourbaki's seminar text. We introduce the combinatorial Kashiwara-Vergne conjecture on the Baker-Campbell-Hausdorff serie. After recalling previous results and consequences, we explain the Alekseev-Meinrenken's proof…
We present a short proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies.
In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.