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A Three Squares Theorem with almost Primes
Author(s) -
Blomer Valentin,
Brüdern Jörg
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004480
Subject(s) - mathematics , prime (order theory) , prime number theorem , cusp (singularity) , fourier series , prime number , sieve (category theory) , mathematics subject classification , number theory , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , geometry
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.