Families of modular eigenforms
Families of modular eigenforms
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模特征形族
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
B. Mazur
中科院分区：
文献类型：
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作者：
F. Gouvêa;B. Mazur
本文是关于计算数理论的MSRI研讨会的一小时讲座的注释的扩展。计算数学的编辑要求我们提交这些注释以供出版，我们非常高兴这样做。我们的原始受众不包括模块化形式领域的专家，我们试图使本文可容纳非X。我们已经对使用MacSyma进行了某些算术连接进行了实验研究。这项调查需要搜索某些高重量的模型特征形式。这些计算构成了我们认为自己可能很有趣的问题。我们是这里的新手，我们寻求更有经验的人来制定类似方式的建议。实际上，我们非常感谢J. F. Mestre，他来帮助我们，并使用Pari大大扩展了我们的计算。1Mestre慷慨地允许我们在本文中介绍他的计算。我们想到的那种家庭（如本讲座的标题）是其原型示例，是经典Eisenstein系列的标准家族，k = 4、6、8，...扩展由OO给出
This article is an expansion of the notes to a one-hour lecture for an MSRI workshop on computational number theory. The editors of Mathematics of Computation kindly asked us to submit these notes for publication, and we are enormously pleased to do so. Our original audience did not consist of experts in the field of modular forms, and we have tried to keep this article accessible to nonexperts. We have made an experimental investigation of certain arithmetic conjec- tures using MACSYMA. This investigation requires a search for certain mod- ular eigenforms of high weight. These computations pose problems which we feel may be interesting on their own. We are novices here, and we seek advice from people more experienced in making computations of an analogous sort. We are, in fact, deeply grateful to J. F. Mestre, who came to our aid and who vastly extended our computations using PARI.1 Mestre has graciously allowed us to present his computations in this article. The kind of families we have in mind, as in the title of this lecture, has as its prototypical example the standard family of classical Eisenstein series of level 1 and weight k for k = 4, 6, 8, ... , whose Fourier expansions are given by oo