# The value of additive forms at prime arguments

• Volume: 13, Issue: 1, page 77-91
• ISSN: 1246-7405

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## Abstract

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Let $f\left(𝐩\right)$ be an additive form of degree $k$ with $s$ prime variables ${p}_{1},{p}_{2},\cdots ,{p}_{s}$. Suppose that $f$ has real coefficients ${\lambda }_{i}$ with at least one ratio ${\lambda }_{i}/{\lambda }_{j}$ 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 $k\ge 6$, Heath-Brown’s improvement on Hua’s Lemma.

## How to cite

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Cook, Roger J.. "The value of additive forms at prime arguments." Journal de théorie des nombres de Bordeaux 13.1 (2001): 77-91. <http://eudml.org/doc/248690>.

@article{Cook2001,
abstract = {Let $f (\mathbf \{p\})$ be an additive form of degree $k$ with $s$ prime variables $p_1,p_2,\dots , p_s$. Suppose that $f$ has real coefficients $\lambda _i$ with at least one ratio $\lambda _i / \lambda _j$ 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 $k \ge 6$, Heath-Brown’s improvement on Hua’s Lemma.},
author = {Cook, Roger J.},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {additive forms; Diophantine inequalities; primes},
language = {eng},
number = {1},
pages = {77-91},
publisher = {Université Bordeaux I},
title = {The value of additive forms at prime arguments},
url = {http://eudml.org/doc/248690},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Cook, Roger J.
TI - The value of additive forms at prime arguments
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 1
SP - 77
EP - 91
AB - Let $f (\mathbf {p})$ be an additive form of degree $k$ with $s$ prime variables $p_1,p_2,\dots , p_s$. Suppose that $f$ has real coefficients $\lambda _i$ with at least one ratio $\lambda _i / \lambda _j$ 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 $k \ge 6$, Heath-Brown’s improvement on Hua’s Lemma.
LA - eng
KW - additive forms; Diophantine inequalities; primes
UR - http://eudml.org/doc/248690
ER -

## References

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