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Displaying similar documents to “Odd values of the Ramanujan τ -function”

The value of additive forms at prime arguments

Roger J. Cook (2001)

Journal de théorie des nombres de Bordeaux

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Let f ( 𝐩 ) be an additive form of degree k with s prime variables p 1 , p 2 , , p s . Suppose that f has real coefficients λ i with at least one ratio λ i / λ j algebraic and irrational. If s is large enough then f takes values close to almost all members of any well-spaced sequence. This complements earlier work of Brüdern, Cook and Perelli (linear forms) and Cook and Fox (quadratic forms). The result is based on Hua’s Lemma and, for k 6 , Heath-Brown’s improvement on Hua’s Lemma.