Sums of Squares Coprime in Pairs

• Autorzy: Brüdern J.

Identyfikatory

DOI

10.4064/ba62-3-3

• Języki publikacji: EN

Abstrakty

EN

Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.

Słowa kluczowe

EN

sums of squares; Kloosterman method; Ternary quadratic forms

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: Vol. 62, no. 3
• Strony: 215--231
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Brüdern J.

• Mathematisches Institut, Bunsenstrasse 3–5, D-37073 Göttingen, Germany

Bibliografia

• [1] V. Blomer, Ternary quadratic forms, and sums of three squares with restricted variables, in: Anatomy of Integers, CRM Proc. Lecture Notes 46, Amer. Math. Soc., Providence, RI, 2008, 1-17.
• [2] V. Blomer and J. Brüdern, A three squares theorem with almost primes, Bull. London Math. Soc. 37 (2005), 507-513.
• [3] J. Brüdern and E. Fouvry, Lagrange's four squares theorem with almost prime variables, J. Reine Angew. Math. 454 (1994), 59-96.
• [4] O. T. O'Meara, Introduction to Quadratic Forms, 3rd printing, Grundlehren Math. Wiss. 117, Springer, New York, 1973.
• [5] H. E. Rose, A Course in Number Theory, 2nd ed., Oxford Univ. Press, Oxford, 1994.
• [6] A. Schinzel, On sums of four coprime squares, Bull. Polish Acad. Sci. Math. 61 (2013), 109-111.
• [7] C. L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta Arith. 1 (1935), 83-86.
• [8] C. L. Siegel, Über die analytische Theorie der quadratischen Formen, Ann. of Math. (2) 36 (1935), 527-606.
• [9] R. C. Vaughan, The Hardy-Littlewood Method, 2nd ed., Cambridge Univ. Press, Cambridge, 1997.
• [10] D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, Berlin, 1981.