A THREE SQUARES THEOREM WITH ALMOST PRIMES

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.