Irrationality of power series for various number theoretic functions

被引：5

作者：

Banks, WD ^{[1
]}

Luca, F

Shparlinski, IE

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico

[3] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

来源：

MANUSCRIPTA MATHEMATICA | 2005年 / 117卷 / 02期

关键词：

Lower Bound; Power Series; Number Theory; Algebraic Geometry; Rational Approximation;

D O I：

10.1007/s00229-005-0564-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study formal power series whose coefficients are taken to be a variety of number theoretic functions, such as the Euler, Mobius and divisor functions. We show that these power series are irrational over Z[X], and we obtain lower bounds on the precision of their rational approximations.

引用

页码：183 / 197

页数：15

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