SOME REMARKS ON THE RIEMANN ZETA FUNCTION AND PRIME FACTORS OF NUMERATORS OF BERNOULLI NUMBERS

被引：1

作者：

Luca, Florian ^{[1
]}

Pizarro-Madariaga, Amalia ^{[2
]}

机构：

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

[2] Univ Valparaiso, Dept Matemat, Valparaiso, Chile

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2012年 / 86卷 / 02期

关键词：

Riemann zeta function; nonholonomicity; primes; Bernoulli numbers;

D O I：

10.1017/S0004972710030054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the sequence {log zeta(n)}(n >= 2) is not holonomic, that is, does not satisfy a finite recurrence relation with polynomial coefficients. A similar result holds for L-functions. We then prove a result concerning the number of distinct prime factors of the sequence of numerators of even indexed Bernoulli numbers.

引用

页码：216 / 223

页数：8

共 5 条

[1]

Ball K, 2001, INVENT MATH, V146, P193, DOI 10.1007/s002220100168

[2] Non-holonomicity of sequences defined via elementary functions [J].

Bell, Jason P. ;

Gerhold, Stefan ;

Klazar, Martin ;

Luca, Florian .

ANNALS OF COMBINATORICS, 2008, 12 (01) :1-16

[3] Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers [J].

Bugeaud, Yann ;

Mignotte, Maurice ;

Siksek, Samir .

ANNALS OF MATHEMATICS, 2006, 163 (03) :969-1018

[4]

Halberstam H., 1974, Lond. Math. Soc. Monographs

[5] An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II [J].

Matveev, EM .

IZVESTIYA MATHEMATICS, 2000, 64 (06) :1217-1269

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