VARIANTS OF ERDOS-SELFRIDGE SUPERELLIPTIC CURVES AND THEIR RATIONAL POINTS

被引：4

作者：

Das, Pranabesh ^{[1
]}

Laishram, Shanta ^{[1
]}

Saradha, N. ^{[2
]}

机构：

[1] Indian Stat Inst, Delhi Ctr, Stat Math Unit, New Delhi 110016, India

[2] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

来源：

MATHEMATIKA | 2018年 / 64卷 / 02期

关键词：

CONSECUTIVE TERMS; PERFECT POWERS; PRODUCTS;

D O I：

10.1112/S0025579317000559

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the superelliptic curves of the form (x + 1) center dot center dot center dot (x + i - l)(x + i + 1) .center dot center dot (x + k) = y(l) with y not equal 0, k >= 3, l >= 2, a prime and for i epsilon [2, k] backslash Omega, we show that l < e(3k). Here Omega denotes the interval [p theta, (k - p theta)), where p theta is the least prime greater than or equal to k/2. Bennett and Siksek obtained a similar bound for i = 1 in a recent paper.

引用

页码：380 / 386

页数：7

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