A Panorama in Number Theory or The View from Baker's Garden: Modular Forms, Elliptic Curves and the ABC -Conjecture
A Panorama in Number Theory or The View from Baker's Garden: Modular Forms, Elliptic Curves and the ABC -Conjecture
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数论全景或贝克花园景观：模形式、椭圆曲线和 ABC 猜想
DOI：
10.1017/cbo9780511542961.010
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
D. Goldfeld
中科院分区：
文献类型：
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作者：
D. Goldfeld
abc猜想最早是由David Masser和Joseph osterl<s:1>在1985年提出的。奇怪的是，虽然这个猜想在上个世纪就可以公式化，但它的发现却是基于现代对函数场和椭圆曲线理论的研究，这表明它是算术代数几何中关于分支的一个陈述。abc猜想似乎与数论中许多不同的和众所周知的问题有关，并且似乎总是处于已知和未知的边界上。我们希望阐明椭圆曲线、模形式和abc猜想之间的美妙联系。
The ABC–conjecture was first formulated by David Masser and Joseph Osterlé (see [Ost]) in 1985. Curiously, although this conjecture could have been formulated in the last century, its discovery was based on modern research in the theory of function fields and elliptic curves, which suggests that it is a statement about ramification in arithmetic algebraic geometry. The ABC–conjecture seems connected with many diverse and well known problems in number theory and always seems to lie on the boundary of what is known and what is unknown. We hope to elucidate the beautiful connections between elliptic curves, modular forms and the ABC–conjecture.