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• W3200022417 abstract "This paper is concerned with the study of diagonal Diophantine inequalities of fractional degree θ, where θ > 2 is real and non-integral. For fixed non-zero real numbers λ i not all of the same sign, we write F ( x ) = λ 1 x 1 θ + ⋯ + λ s x s θ . For a fixed positive real number τ, we give an asymptotic formula for the number of positive integer solutions of the inequality | F ( x ) | < τ inside a box of side length P. Moreover, we investigate the problem of representing a large positive real number by a positive definite generalised polynomial of the above shape. A key result in our approach is an essentially optimal mean value estimate for exponential sums involving fractional powers of integers." @default.
• W3200022417 created "2021-09-27" @default.
• W3200022417 creator A5040833825 @default.
• W3200022417 date "2021-09-10" @default.
• W3200022417 modified "2023-09-26" @default.
• W3200022417 title "DIOPHANTINE INEQUALITIES OF FRACTIONAL DEGREE" @default.
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• W3200022417 doi "https://doi.org/10.1112/mtk.12112" @default.
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