Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


An explicit modular equation in two variables and Hilbert's twelfth problem

Author: Harvey Cohn
Journal: Math. Comp. 38 (1982), 227-236
MSC: Primary 10D20; Secondary 12A65
MathSciNet review: 637301
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Hilbert modular function field over $ {\mathbf{Q}}(\surd 2)$ has generators satisfying modular equations when the arguments are multiplied by factors of norm two. These equations are found by machine use of Fourier series and are further used to show computationally that Weber's ring class field theory for rationals has an illustration of Hecke's type for $ {\mathbf{Q}}(\surd 2)$. This has bearing on Hubert's twelfth problem, the generation of algebraic fields by transcendental functions.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10D20, 12A65

Retrieve articles in all journals with MSC: 10D20, 12A65

Additional Information

PII: S 0025-5718(1982)0637301-5
Article copyright: © Copyright 1982 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia