CONSTRUCTION OF DIAGONAL QUINTIC THREEFOLDS WITH INFINITELY MANY RATIONAL POINTS

被引：0

作者：

Ulas, Maciej ^{[1
]}

机构：

[1] Jagiellonian Univ, Inst Math, Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

MATHEMATICS OF COMPUTATION | 2024年 / 93卷 / 349期

关键词：

Diagonal quintic threefolds; polynomial solutions; quadratic forms; Gro<spacing diaeresis> bner basis;

D O I：

10.1090/mcom/3953

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we present a construction of an infinite family of diagonal quintic threefolds defined over Q each containing infinitely many rational points. As an application, we prove that there are infinitely many quadruples B = (B-0, B-1, B-2, B-3) of co-prime integers such that for a suitable chosen integer b (depending on B), the equation B0Xo5 + B1X15 + B2X25 + B3X35 = b has infinitely many positive integer solutions.

引用

页码：2503 / 2511

页数：9