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

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Small zeros of additive forms in many variables

Author: Wolfgang M. Schmidt
Journal: Trans. Amer. Math. Soc. 248 (1979), 121-133
MSC: Primary 10B30; Secondary 10J10
MathSciNet review: 521696
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if s is large as a function of k and of $ \varepsilon > 0$, then the diophantine equation $ {a_1}{x_1}^k + \cdots + {a_s}x_s^k = {b_1}y_1^k + \cdots + {b_s}y_s^k$ with positive coefficients $ {a_1}, \ldots ,{a_s}$, $ {b_1}, \ldots ,{b_s}$ has a nontrivial solution in nonnegative integers $ {x_1}, \ldots ,{x_s}$, $ {y_1}, \ldots ,{y_s}$ not exceeding $ {m^{\left( {1/k} \right) + \varepsilon }}$, where m is the maximum of the coefficients.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 10B30, 10J10

Retrieve articles in all journals with MSC: 10B30, 10J10

Additional Information

PII: S 0002-9947(1979)0521696-3
Article copyright: © Copyright 1979 American Mathematical Society