9 papers · 1 filter
Ramanujan-type identities for alternating Hurwitz zeta functions
Meng Yuan, Su Hu, Min-Soo Kim
Around 1910, in an unpublished manuscript, Ramanujan proposed the following identity for : \[ \begin{aligned} α^{-n}\,&\left\{\dfrac{1}{2}\,ζ(2n + 1) + \sum_{m = 1}^{\inft…
On the reciprocity law in
Su Hu, Enci Wang
In 1991, Rousseau gave a new proof of Gauss's quadratic reciprocity by comparing two distinct coset representations of the group $(\mathbb{Z}_{p}^{*} \times \mathbb{Z}_{q}^{*}) / U…
An analogue of Ramanujan's identity for Bernoulli-Carlitz numbers
Su Hu, Min-Soo Kim
In his second notebook, Ramanujan discovered the following identity for the special values of at the odd positive integers \begin{equation*}\begin{aligned}α^{-m}\,\left\{\…
On the properties of alternating invariant functions
Haiqing Zhu, Su Hu, Min-Soo Kim
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer }, \end{align*} are named the…
On -adic spectral zeta functions
Su Hu, Min-Soo Kim
The spectral zeta functions have been found many application in several branches of modern physics, including the quantum field theory, the string theory and the cosmology. In this…
Sums of infinite series involving the Dirichlet lambda function
Su Hu, Min-Soo Kim
The Dirichlet lambda function is defined for by \[ λ(s) = \sum_{n=0}^{\infty} \frac{1}{(2n+1)^s}. \] This function was initially studied by Euler on t…