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Sums of Two Squares of Sums of Two Squares

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From Arithmetic to Zeta-Functions

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Abstract

This article determines the order of magnitude of integers not exceeding x that can be written as sums of two squares of integers that are themselves sums of two squares. The tools include Selberg’s sieve and contour integration in the spirit of the Selberg-Delange method.

Dedicated to Wolfgang Schwarz

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References

  1. H. Iwaniec, E. Kowalski, Analytic Number Theory. American Mathematical Society Colloquium Publications, vol. 53 (American Mathematical Society, Providence, 2004)

    Google Scholar 

  2. E. Landau, Über die Zahlentheoretische Funktion φ(n) und ihre Beziehung zum Goldbachschen Satz. Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. 1900, 177–186 (1900)

    Google Scholar 

  3. E. Landau, Über die Zerlegung der Zahlen in zwei Quadrate. Annali di Matematica 20 (1), 1–28 (1913)

    Article  MATH  Google Scholar 

  4. J. Liu, Y. Ye, Perron’s formula and the prime number theorem for automorphic L-functions. Pure Appl. Math. Q. 3 (2), 481–497 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. P. Shiu, A Brun-Titschmarsh theorem for multiplicative functions. J. Reine Angew. Math. 313, 161–170 (1980)

    MathSciNet  MATH  Google Scholar 

  6. G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory. Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

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Acknowledgements

I am very grateful to Prof. Valentin Blomer for suggesting this topic to me and his constant advice and encouragement.

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Authors and Affiliations

  1. Universität Göttingen, Bunsenstr. 3-5, 37073, Göttingen, Germany

    Rebecca Ulrike Jakob

Authors
  1. Rebecca Ulrike Jakob
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Correspondence to Rebecca Ulrike Jakob .

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Editors and Affiliations

  1. Institut für Mathematik und Angewandte Informatik, Stiftung Universität Hildesheim, Hildesheim, Germany

    Jürgen Sander

  2. Institut für Mathematik, Julius-Maximilians Universität Würzburg, Würzburg, Germany

    Jörn Steuding

  3. Institut für Mathematik, Julius-Maximilians Universität Würzburg, Würzburg, Germany

    Rasa Steuding

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Jakob, R.U. (2016). Sums of Two Squares of Sums of Two Squares. In: Sander, J., Steuding, J., Steuding, R. (eds) From Arithmetic to Zeta-Functions. Springer, Cham. https://doi.org/10.1007/978-3-319-28203-9_14

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