Values of \(p\)-adic \(L\)-functions at positive integers and \(p\)-adic log multiple gamma functions (Q1319192)

In the late 1970s, Diamond expressed special values of \(p\)-adic \(L\)- functions at positive integers in terms of the \(p\)-adic log gamma function. In this paper, the author extends the work of Diamond to a class of \(p\)-adic \(L\)-functions in several variables (previously defined by the author). He expresses special values of these \(L\)-functions at positive integers in terms of \(p\)-adic log multiple gamma functions. Since the \(p\)-adic \(L\)-function of a totally real number field can be expressed in terms of these multivariable \(p\)-adic \(L\)-functions, their special values at positive integers can also be expressed in this manner.