10 papers
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Around 1910, in an unpublished manuscript, Ramanujan proposed the following identity for : \[ \begin{aligned} α^{-n}\,&\left\{\dfrac{1}{2}\,ζ(2n + 1) + \sum_{m = 1}^{\inft…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…
On path integrals for wave functions taking -adic values
Su Hu, Min-Soo Kim
In this paper, we construct a -adic path integral via -adic multiple integrals. This integral describes the evolution of a wave function , which is defined as a map fr…
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…