Taiwanese Journal of Mathematics

THE INTEGER PARTS OF A NONLINEAR FORM WITH MIXED POWERS 3 AND k

Baiyun Su and Weiping Li

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Abstract

Using the Davenport-Heilbronn circle method, we show that if $\lambda_1,\cdots,\lambda_5$ are positive real numbers, at least one of the ratios $\lambda_i/\lambda_j(1\leq i\lt j\leq 5)$ is irrational, then, for arbitrary positive integer $k\geq 4$, the integer parts of $\lambda_1 x_1^3 + \lambda_2 x_2^3 + \lambda_3 x_3^3 + \lambda_4 x_4^3 +\lambda_5 x_5^k$ are prime infinitely often for natural numbers $x_1,\cdots,x_5$.

Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 497-507.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499706400

Digital Object Identifier
doi:10.11650/tjm.18.2014.2794

Mathematical Reviews number (MathSciNet)
MR3188517

Zentralblatt MATH identifier
1357.11039

Subjects
Primary: 11D75: Diophantine inequalities [See also 11J25] 11P55: Applications of the Hardy-Littlewood method [See also 11D85]

Keywords
Davenport-Heilbronn circle method integer variables Diophantine approximation

Citation

Su, Baiyun; Li, Weiping. THE INTEGER PARTS OF A NONLINEAR FORM WITH MIXED POWERS 3 AND k. Taiwanese J. Math. 18 (2014), no. 2, 497--507. doi:10.11650/tjm.18.2014.2794. https://projecteuclid.org/euclid.twjm/1499706400


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References

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