### Abstract

Recent developments in the theory of diophantine inequalities and the Davenport-Heilbronn method are discussed and then directed toward specific inequalities of definite character. Special emphasis is on the value-distribution of diagonal forms near thin test sequences.

Original language | English |
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Title of host publication | NUMBER THEORY: DREAMING IN DREAMS |

Editors | T Aoki, S Kanemitsu, JY Liu |

Place of Publication | SINGAPORE |

Publisher | World Scientific Publishing Co. |

Pages | 20-79 |

Number of pages | 60 |

Publication status | Published - 2010 |

Event | 5th China-Japan Seminar on Number Theory - Higashiosaka, Japan Duration: 27 Aug 2008 → 31 Aug 2008 |

### Publication series

Name | Series on Number Theory and Its Applications |
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Publisher | WORLD SCIENTIFIC PUBL CO PTE LTD |

Volume | 6 |

ISSN (Print) | 1793-3161 |

### Conference

Conference | 5th China-Japan Seminar on Number Theory |
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Country | Japan |

Period | 27/08/08 → 31/08/08 |

### Keywords

- LATTICE POINT PROBLEMS
- MEAN-VALUE THEOREM
- WARING PROBLEM
- GOLDBACH NUMBERS
- PRIME VARIABLES
- QUADRATIC-FORMS
- CUBES
- POLYNOMIALS
- EQUATIONS
- VALUES

## Cite this

Bruedern, J., Kawada, K., & Wooley, T. D. (2010). ADDITIVE REPRESENTATION IN THIN SEQUENCES, VIII: DIOPHANTINE INEQUALITIES IN REVIEW. In T. Aoki, S. Kanemitsu, & JY. Liu (Eds.),

*NUMBER THEORY: DREAMING IN DREAMS*(pp. 20-79). (Series on Number Theory and Its Applications; Vol. 6). World Scientific Publishing Co..