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)


Algebraic numbers close to both 0 and $ 1$

Author: D. Zagier
Journal: Math. Comp. 61 (1993), 485-491
MSC: Primary 11R06; Secondary 11R04, 12D10
MathSciNet review: 1197513
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A recent theorem of Zhang asserts that

$\displaystyle H(\alpha ) + H(1 - \alpha ) \geq C$

for all algebraic numbers $ \alpha \ne 0,1, (1 \pm \sqrt { - 3} )/2$, and some constant $ C > 0$. An elementary proof of this, with a sharp value for the constant, is given (the optimal value of C is $ \tfrac{1}{2}\log (\tfrac{1}{2}(1 + \sqrt 5 )) = 0,2406 \ldots $, attained for eight values of $ \alpha $) and generalizations to other curves are discussed.

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

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 11R06, 11R04, 12D10

Retrieve articles in all journals with MSC: 11R06, 11R04, 12D10

Additional Information

PII: S 0025-5718(1993)1197513-9
Article copyright: © Copyright 1993 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