A THREE SQUARES THEOREM WITH ALMOST PRIMES

2005/08/01 by Valentin Blomer, VALENTIN BLOMER, JÖRG BRÜDERN +1 · 1 citation
Mathematics · #Analytic Number Theory Research #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory

paper · doi:10.1112/s0024609305004480

Abstract

As an application of the vector sieve and uniform estimates on the Fourier coefficients of cusp forms of half-integral weight, it is shown that any sufficiently large number n ≡ 3 (mod 24) with 5 ∤ n is expressible as a sum of three squares of integers having at most 521 prime factors. 2000 Mathematics Subject Classification 11P05, 11N36, 11N75, 11E25.

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• On the equation x₁² + x₂² + x₃² + x₄² = N with variables such that x₁ x₂ x₃ x₄ + 1 is an almost-prime

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