In this work we consider the problem from the point of view of analytic aspects of L-functions instead. We show that Hilbert's tenth problem for rings of integers of number fields is unsolvable, conditional to the following conjectures for L-functions of elliptic curves: the automorphy ...
A comprehensive treatment of elliptic functions is linked by these notes to a study of their application to elliptic curves. This approach provides geometers with the opportunity to acquaint themselves with aspects of their subject virtually ignored by other texts. The exposition is clear and logicall...
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Elliptic Curves and the Special Values of L-functions (ICTS 2021)共计23条视频,包括:Introduction to Elliptic Curves 1 by Anupam Saikia、Introduction to Elliptic Curves 2 by Anupam Saikia、Introduction to Elliptic Curves 3 by Anupam Saikia等,UP主更多精
https://www.icts.res.in/program/ecl2022/talks ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS The program plans to focus on recent developments in the arithmetic of Elliptic curves and special v
functions on elliptic curves have the same number of zeros as poles, df f can have no zeros. The function x on E has a double zero at each point of order 2 and a double pole at P ∞ . Therefore dx has zeros at each point of order 2 and a triple pole at P ∞ . Thus f f ...
Elliptic Curves, Modular Forms, and Their L-functions 2025 pdf epub mobi 用户评价 评分☆☆☆ 一本薄书介绍三个大对象,必须是导引书,但导引的不错。 评分☆☆☆ 最有用的部分是介绍Sage的附录 评分☆☆☆ 最有用的部分是介绍Sage的附录 评分☆☆☆ 最...
If we implemented a cryptosystem using the functions as so far described, we would have a very slow cryptosystem. The reason being that modular inversions—that is, computing 1/x modulo a prime—is a very slow operation, often comparable to dozens of field multiplications. To solve this ...
A new elliptic curve was discovered, breaking a record set in 2006 and pushing at the limits of current methods for finding them. Here’s some background on the curves and some of the characters involved. This year also saw a proof of the geometric Langlands conjecture, and this article ex...
ECC(Elliptic Curves Cryptography,椭圆曲线加密)是一种公开密钥算法。1985年,Neal Koblitz和Victor Miller分别独立提出了ECC。ECC是目前最具发展和应用潜力的公钥密码,其数学基础是椭圆曲线离散对数问题(ECDLP)。 一、从平行线谈起 平行线,永不相交。没有人怀疑把:)不过到了近代这个结论遭到了质疑。平行线会不会在很...