44 2033180199
All submissions of the EM system will be redirected to Online Manuscript Submission System. Authors are requested to submit articles directly to Online Manuscript Submission System of respective journal.
Journal of Pure and Applied Mathematics

Sign up for email alert when new content gets added: Sign up

On the Injectivity of an Integral Operator Connected to Riemann Hypothesis

Author(s): Dumitru Adam*

The equivalent formulation of the Riemann Hypothesis (RH) given by Alcantara-Bode (1993) states: RH holds if and only if the integral operator on the Hilbert space L2 (0, 1) having the kernel function defined by the fractional part of (y/x) is injective. This formulation reduced one of the most important unsolved problems in pure mathematics to a problem whose investigation could be made by standard techniques of the applied mathematics.

The method introduced to deal with, is based on a result obtained in this paper: an operator linear, bounded, Hermitian on a separable Hilbert space strict positive definite on a dense family of including subspaces, subspaces on which the sequence of the ratios between the smallest and largest eigenvalues of the operator restrictions on the family is bounded inferior by a strict positive constant, is injective. Using a version of the generic method for integral operators on L2 (0, 1) we proved the injectivity of the integral operator used in the equivalent formulation of the RH.

Full-Text | PDF
Google Scholar citation report
Citations : 16

Journal of Pure and Applied Mathematics received 16 citations as per Google Scholar report

Journal of Pure and Applied Mathematics peer review process verified at publons