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A Matrix Related to the Theorem of Fermat and the Goldbach Conjecture

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Part of the book series: Developments in Mathematics ((DEVM,volume 28))

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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.

Mathematics Subject Classification: 11A25, 11A41

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References

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    Hershel M. Farkas

Authors
  1. Hershel M. Farkas
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Correspondence to Hershel M. Farkas .

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Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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Dedicated to the Memory of Leon Ehrenpreis

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Farkas, H.M. (2013). A Matrix Related to the Theorem of Fermat and the Goldbach Conjecture. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_9

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