“Gronwall's Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Gronwall's Theorem

释义

Gronwall's Theorem

Let be the Divisor Function. Then

where

is the Euler-Mascheroni Constant. Ramanujan independently discovered a less precise versionof this theorem (Berndt 1994). Robin (1984) showed that the validity of the inequality

for

is equivalent to the Riemann Hypothesis.

References

Berndt, B. C. Ramanujan's Notebooks: Part I. New York: Springer-Verlag, p. 94, 1985.

Gronwall, T. H. ``Some Asymptotic Expressions in the Theory of Numbers.'' Trans. Amer. Math. Soc. 37, 113-122, 1913.

Nicholas, J.-L. ``On Highly Composite Numbers.'' In Ramanujan Revisited: Proceedings of the Centenary Conference (Ed. G. E. Andrews, B. C. Berndt, and R. A. Rankin). Boston, MA: Academic Press, pp. 215-244, 1988.

Robin, G. ``Grandes Valeurs de la fonction somme des diviseurs et hypothèse de Riemann.'' J. Math. Pures Appl. 63, 187-213, 1984.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。