Tagged Questions
8
votes
2answers
171 views
How can I prove my conjecture for the coefficients in $t(x)=\log(1+\exp(x)) $?
I'm considering the transfer-function
$$ t(x) = \log(1 + \exp(x)) $$
and find the beginning of the power series (simply using Pari/GP) as
$$ t(x) = \log(2) + 1/2 x + 1/8 x^2 – 1/192 x^4 + 1/2880 x^6 - ...
7
votes
1answer
189 views
Reference request: $L$-series and $\zeta$-functions
Does anyone know a good book, lecture note, article etc. on $L$-series (Dirichlet, Hecke, Artin) and $\zeta$-functions in number theory? I'm especially interested in material explaining the following:
...
10
votes
2answers
310 views
Two Dirichlet's series related to the Divisor Summatory Function and to the Riemann's zeta-function, $\zeta(s)$
Considering the $\textit{Divisor Summatory Function}$, $D(n)$, defined as
$$
D(n) = \sum_{k=1}^{n}d(k) ,
$$
where
$$
d(n) = \sum_{k|n}^{n}1.
$$
One can observe the following pattern in the values of ...
