Related papers: Towards a proof of the Riemann Hypothesis
The Riemann hypothesis is, and will hopefully remain for a long time, a great motivation to uncover and explore new parts of the mathematical world. After reviewing its impact on the development of algebraic geometry we discuss three…
We improve constants in the Rademacher-Menchov inequality.
Detecting semantic arguments of a predicate word has been conventionally modeled as a sentence-level task. The typical reader, however, perfectly interprets predicate-argument relations in a much wider context than just the sentence where…
We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…
The Riemann hypothesis is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems. it is also one of the Clay Mathematics Institute's Millennium Prize Problems. Some mathematicians consider it the most important…
We use a spectral theory perspective to reconsider properties of the Riemann zeta function. In particular, new integral representations are derived and used to present its value at odd positive integers.
The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
The goal of this paper is to prove the Riemann-Roch isomorphism for the higher equivariant K-theory of varieties with action of a linear algebraic group.
We formulate and prove a version of the celebrated Coifman-Rochberg-Weiss commutator theorem for the real method of interpolation
There have been a number of recent works on the theory of period polynomials and their zeros. In particular, zeros of period polynomials have been shown to satisfy a "Riemann Hypothesis" in both classical settings and for cohomological…
Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…
A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in…
This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".
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.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the…
This article contains work associated with a resolution of the Riemann hypothesis, following work by Taylor \cite{prt}, Lagarias and Suzuki \cite{lagandsuz} and Ki \cite{ki}, as well as Pustyl'nikov \cite{pust, pust2} and Keiper…
We utilize a combination of integral transforms, including the Laplace transform, with some classical results in analytic number theory concerning the Riemann $\xi$-function, to obtain a new integral equation. We also provide a new proof of…
The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].