Rocky Mountain Journal of Mathematics

Gauss's three squares theorem involving almost-primes

Yingchun Cai

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Rocky Mountain J. Math., Volume 42, Number 4 (2012), 1115-1134.

First available in Project Euclid: 27 September 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N36: Applications of sieve methods 11P05: Waring's problem and variants


Cai, Yingchun. Gauss's three squares theorem involving almost-primes. Rocky Mountain J. Math. 42 (2012), no. 4, 1115--1134. doi:10.1216/RMJ-2012-42-4-1115.

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  • V. Blomer, Ternary quadratic forms, and sums of three squares with restricted variables, CRM Proc. Lect. Notes 46 (2008), 1-17.
  • V. Blomer and J. Br\Hudern, A three squares theorem with almost primes, Bull. London Math. Soc. 37 (2005), 507-513.
  • J. Br\Hudern and E. Fouvry, Lagrange's four squares theorem with almost prime variables, J. reine angew Math. 454 (1994), 59-96.
  • H. Halberstam, D.R. Heath-Brown and H.E. Richert, Almost-primes in short intervals, in Recent progress in analytic number theory, Academic Press, New York, 1981.
  • G. Harman and A.V. Kumchev, On sums of squares of primes, Math. Proc. Cambr. Philos. Soc. 140 (2006), 1-13.
  • L.K. Hua, Some results in additive prime number theory, Quart. J. Math. Oxford. 9 (1938), 68-80.
  • H. Iwaniec, Rosser's sieve, Acta Arith. 36 (1980), 171-202.
  • –––, A new form of the error term in the linear sieve, Acta Arith. 36 (1980), 307-320.
  • G.S. L\Hu, Gauss's three squares theorem with almost prime variables, Acta. Arith. 128 (2007), 391-399.
  • C.L. Siegel, \HUber die analytische Theorie quadratischer Formen I, Ann. Math. 36 (1935), 527-606.
  • –––, \HUber die Klassenzahl quadratischer Zahlkőrper, Acta. Arith. 1 (1935), 83-86. \noindentstyle