L2 Majorant Principles

  • Hugh L. Montgomery
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 25)


In this short historical note, we discuss an important majorant principle introduced by Erdős & Fuchs [1].


London Math Fourier Expansion Arithmetic Function Michigan Math Complex Exponential 
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  1. [1]
    P. Erdős & W. H. J. Fuchs, On a problem of additive number theory, J. London Math. Soc. 31 (1956), 67–73.CrossRefMathSciNetGoogle Scholar
  2. [2]
    P. Erdős & P. Turán, On a problem of Sidon in additive number theory, and some related problems, J. London Math. Soc. 16 (1941), 212–215; addendum, ibid. 19 (1944), 208.CrossRefMathSciNetGoogle Scholar
  3. [3]
    G. Halász, Über die Mittelwerte multiplicativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar. 19 (1968), 365–403.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    G. H. Hardy, On the expression of a number as a sum of two squares, Quart. J. Math. 46 (1915), 263–283.zbMATHGoogle Scholar
  5. [5]
    E. K. Hayashi, Omega theorems for the iterated additive convolution of a non-negative arithmetic function, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1973.Google Scholar
  6. [6]
    B. F. Logan, An interference problem for exponentials, Michigan Math. J. 35 (1988), 369–393.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    H. L. Montgomery & R. C. Vaughan, On the Erdős-Fuchs theorems, A Tribute to Paul Erdős. Cambridge University Press, 1990.Google Scholar
  8. [8]
    Norbert Wiener, Collected Works with Commentaries, Vol. II, MIT Press, 1979.Google Scholar
  9. [9]
    N. Wiener & A. Winter, On a local L 2-variant of Ikeharaś theorem, Rev. Math. Cuyana 2 (1956), 53–59.MathSciNetGoogle Scholar

Copyright information

© János Bolyai Mathematical Society and Springer-Verlag 2013

Authors and Affiliations

  • Hugh L. Montgomery
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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