The Manin–Peyre conjecture for certain multiprojective hypersurfaces

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-03-20 DOI:10.1142/s1793042124500623

Xiaodong Zhao

引用次数: 0

Abstract

By the circle method, an asymptotic formula is established for the number of integer points on certain hypersurfaces within multiprojective space. Using Möbius inversion and the modified hyperbola method, we prove the Manin–Peyre conjecture on the asymptotic behavior of the number of rational points of bounded anticanonical height for certain smooth hypersurfaces in the multiprojective space of sufficiently large dimension.

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某些多射超曲面的马宁-佩雷猜想

通过圆法，建立了多射空间内某些超曲面上整数点数的渐近公式。利用莫比乌斯反演法和修正双曲线法，我们证明了马宁-佩雷猜想，即在足够大维度的多射空间中，某些光滑超曲面上有界反锥高的有理点数的渐近行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

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