A matrix related to the theorem of fermat and the Goldbach conjecture

Hershel M. Farkas

doi:10.1007/978-1-4614-4075-8_9

A matrix related to the theorem of fermat and the Goldbach conjecture

Hershel M. Farkas

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In this chapter, we show how converting a Lambert series to a Taylor series introduces a matrix similar to the Redheffer matrix, whose inverse is determined by the Mobius function. A variant of the Mobius function which generalizes the Littlewood function along with this matrix allows one to count the integral solutions to the equation x^l + y^l = r. Similar ideas hold for the Goldbach conjecture.

Original language	English
Title of host publication	From Fourier Analysis and Number Theory to Radon Transforms and Geometry
Subtitle of host publication	In Memory of Leon Ehrenpreis
Editors	Hershel Farkas, Marvin Knopp, Robert Gunning, B.A Taylor
Pages	217-232
Number of pages	16
DOIs	https://doi.org/10.1007/978-1-4614-4075-8_9
State	Published - 2013

Publication series

Name	Developments in Mathematics
Volume	28
ISSN (Print)	1389-2177

Keywords

Fermat's theorem
Goldbach conjecture
Littlewood function
Mobius function

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10.1007/978-1-4614-4075-8_9

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A matrix related to the theorem of fermat and the Goldbach conjecture. / Farkas, Hershel M.
From Fourier Analysis and Number Theory to Radon Transforms and Geometry: In Memory of Leon Ehrenpreis. ed. / Hershel Farkas; Marvin Knopp; Robert Gunning; B.A Taylor. 2013. p. 217-232 (Developments in Mathematics; Vol. 28).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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A matrix related to the theorem of fermat and the Goldbach conjecture

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Keywords

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