20/02/13 18:02:42.81 Di2gg/DV.net
>>377 補足
おれだったら、研究するなら、最低でも下記は読み込むけどね
（2013年なので、これでは足りないけどね）
URLﾘﾝｸ(arxiv.org)
EULER’S CONSTANT: EULER’S WORK AND MODERN DEVELOPMENTS
JEFFREY C. LAGARIAS Date: October 10, 2013.
(抜粋)
Abstract. This paper has two parts. The first part surveys Euler’s work on the constant γ = 0.57721... bearing his name, together with some of his related work on the
gamma function, values of the zeta function, and divergent series. The second part
describes various mathematical developments involving Euler’s constant, as well as
another constant, the Euler-Gompertz constant. These developments include connections with arithmetic functions and the Riemann hypothesis, and with sieve methods,
random permutations, and random matrix products. It also includes recent results on
Diophantine approximation and transcendence related to Euler’s constant.
Contents
1. Introduction 2
2. Euler’s work 4
2.1. Background 4
2.2. Harmonic series and Euler’s constant 5
2.3. The gamma function 11
2.4. Zeta values 13
2.5. Summing divergent series: the Euler-Gompertz constant 22
2.6. Euler-Mascheroni constant; Euler’s approach to research 27
3. Mathematical Developments 28
3.1. Euler’s constant and the gamma function 28
3.2. Euler’s constant and the zeta function 32
3.3. Euler’s constant and prime numbers 35
3.4. Euler’s constant and arithmetic functions 36
3.5. Euler’s constant and sieve methods: the Dickman function 39
3.6. Euler’s constant and sieve methods: the Buchstab function 42
3.7. Euler’s constant and the Riemann hypothesis 44
3.8. Generalized Euler constants and the Riemann hypothesis 46
3.9. Euler’s constant and extreme values of ζ(1 + it) and L(1, χ?d) 48
3.10. Euler’s constant and random permutations: cycle structure 51
略
4. Concluding remarks 77