Related papers: Pseudodifferential arithmetic and the Riemann hypo…

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…

This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576

Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…

An analysis of 2,765 articles published in four math journals from 1997 to 2005 indicate that articles deposited in the arXiv received 35% more citations on average than non-deposited articles (an advantage of about 1.1 citations per…

This is a sequel to arXiv:1308.3604. We study applications to limit multiplicity generalizing the results of arXiv:1208.2257.

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

We give a general Lie-theoretic construction for anti-invariant almost Hermitian Riemannian submersions, anti-invariant quaternion Riemannian submersions, anti-invariant para-Hermitian Riemannian submersions, anti-invariant para-quaternion…

This paper has been withdrawn due to a critical error discovered in Theorem 4.21.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…

The paper gives a counter-example to the relative version of the Manin-Mumford conjecture.

In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].

This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2

Baez-Duarte reformulated the Riemann hypothesis as a statement about a Hilbert space distance, involving the integer dilations of the "fractional part" function. Under the assumption of the Riemann hypothesis, we improve on the currently…

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results…

This paper has been withdrawn by the author, due to a crucial error in page 5.

In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…

This paper proves the existence of infinitely many Perrin pseudoprimes, as conjectured by Adams and Shanks in 1982. The theorem proven covers a general class of pseudoprimes based on recurrence sequences. The result uses ingredients of the…

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.