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We study analytic properties of multiple zeta-functions of generalizedHurwitz-Lerch type. First, as a special type of them, we consider multiplezeta-functions of generalized Euler-Zagier-Lerch type and investigate theiranalytic properties which were already announced in our previous paper. Next wegive `desingularization' of multiple zeta-functions of generalizedHurwitz-Lerch type, which include those of generalized Euler-Zagier-Lerch type,the Mordell-Tornheim type, and so on. As a result, the desingularized multiplezeta-function turns out to be an entire function and can be expressed as afinite sum of ordinary multiple zeta-functions of the same type. Asapplications, we explicitly compute special values of desingularized doublezeta-functions of Euler-Zagier type. We also extend our previous resultsconcerning a relationship between $p$-adic multiple $L$-functions and $p$-adicmultiple star polylogarithms to more general indices with arbitrary (notnecessarily all positive) integers.

Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers