欧拉常数作为黎曼ζ函数在极点处的重整化值。与Dirichlet L-函数有关的代数
Euler constant as a renormalized value of Riemann zeta function at its pole. Rationals related to Dirichlet L-functions
摘要：
我们相信欧拉常数不仅仅是1中的黎曼ζ函数的“重整化”值。在某种意义上，我们将澄清，它实际上是正常的和自然的值1。在本文中，我们首先提出了一个函数的极限定义，其值与黎曼ζ函数的值一致的任何地方，除了在1，我们的极限定义产生的欧拉常数。由于在文献中可以找到一种以上的方法来规范的zeta函数的值在s=1，我们给渐近展开，凭借一些扩展的类比，欧拉常数似乎是真正的“重整化”值。作为这种类比的一个突出的例子，我们提出了一个扩展的对数函数的基础上欧拉常数和zeta函数的所有值在奇数正整数，其中所有这些大概无理数伴随着相应的订单调和数。本文的另一个目的是展示序列的有理数，往往是相同的，出现在计算相关的狄利克雷L-函数。在这里，一个连接与刘维lambda函数似乎已经发现。因此，我们提出的问题，可能有用的扩展刘维lambda函数的有理数。.
英文摘要：
We believe that Euler constant is not just the "renormalized" value of the Riemann zeta function in 1. In a sense that we shall clarify it is in fact the normal and natural value of zeta of 1. In this paper we first propose a limit definition of a function whose values coincide everywhere with those of the Riemann zeta function, save in 1, where our limit definition yields the Euler constant. Since in the literature one can find more than one way to regularize the value of the zeta function at s=1, we give asymptotic expansions where, by dint of some extended analogies, Euler constant appears to be the true "renormalized" value. As a striking example of such analogies, we propose an expansion of the logarithm function based on Euler constant and on all values of the zeta function at odd positive integers, in which all these presumably irrational numbers are accompanied by Harmonic numbers of corresponding orders. The other aim of this paper is to show how sequences of rationals, often the same, arise in computations related to Dirichlet L-functions. Here, a connection with the Liouville lambda function appears to have been found. Thus we raise the question about the possible usefulness of an extension of the Liouville lambda function to rationals. .
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