Manjul Bhargava had generalized the factorial function in number-theoretic context in this paper. At the end of the paper, he mentions some interesting problems associated with the generalized factorials.
I am particularly interested in the analogues of the Stirling's formula, Binomial coefficients and exponential function. So I want to know whether these problems are still unresolved and if so, then what is the present status of the research regarding these problems.