The non-congruent numbers via Monsky’s formula-Reference-Cited by-同舟云学术

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The non-congruent numbers via Monsky’s formula

Published:2019-04-29 Issue:04 Volume:15 Page:677-711
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Cheng Weidong¹,Guo Xuejun¹

Affiliation:

1. Department of Mathematics, Nanjing University, 22 Hankou Road, Gulou Nanjing 210093, Jiangsu, P. R. China

Abstract

This paper gives some new families of non-congruent numbers with arbitrarily many prime divisors. The main idea is based on Monsky’s formula for the 2-Selmer rank of congruent elliptic curves.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119500362

Reference19 articles.

1. Non-congruent numbers, odd graphs and the Birch-Swinnerton-Dyer conjecture

2. On elliptic curves y2=x3−n2x with rank zero

3. New series of odd non-congruent numbers

4. CONSTRUCTING NEW NON-CONGRUENT NUMBERS BY GRAPH THEORY

5. The size of Selmer groups for the congruent number problem

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Monsky Matrices and Non-congruent Numbers;Algebra Colloquium;2024-05-29

2. FAMILIES OF NON-CONGRUENT NUMBERS WITH ARBITRARILY MANY TRIPLETS OF PRIME FACTORS;Kyushu Journal of Mathematics;2024

3. Families of non-congruent numbers with odd prime factors of the form 8k + 3;Journal of Number Theory;2021-10

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