Desingularization of complex multiple zeta-functions, fundamentals of pp-adic multiple LL-functions, and evaluation of their special values

This paper deals with a multiple version of zeta- and L-functions both in the complex case and in the p-adic case: [I] Our motivation in the complex case is to find suitable rigorous meaning of the values of multivariable multiple zeta-functions (MZFs) at non-positive integer points. (a) We reveal that MZFs turn to be entire on the whole space after taking the desingularization. Further we show that the desingularized function is given by a suitable finite linear combination of MZFs with some arguments shifted. It is also shown that specific combinations of Bernoulli numbers attain the special values at their non-positive integers of the desingularized ones. (b) Twisted MZFs can be continued to entire functions and their special values at non-positive integer points can be explicitly calculated. [II] Our work in the p-adic case is to develop the study on analytic side of the Kubota-Leopoldt p-adic L-functions (pLFs) into the multiple setting. We construct p-adic multiple L-functions (pMLFs), multivariable versions of their pLFs, by using a specific p-adic measure. We establish their various fundamental properties: (a) We establish their intimate connection with the above complex MZFs by showing that the special values of pMLFs at non-positive integers are expressed by the twisted multiple Bernoulli numbers, the special values of the complex MZFs at non-positive integers. (b) We extend Kummer congruence for Bernoulli numbers to congruences for the twisted multiple Bernoulli numbers. (c) We extend the vanishing property of the Kubota-Leopoldt pLFs with odd characters to our pMLFs. (d) We establish their close relationship with the p-adic twisted multiple polylogarithms (pTMPLs) by showing that the special values of pMLFs at positive integers are described by those of pTMPLs at roots of unity, which generalizes the previous result of Coleman in the single variable case.Comment: This article was divided into the complex part arXiv:1508.06920 and the p-adic part arXiv:1508.0718

Protein transduction technology: a novel therapeutic perspective.

The direct intracellular delivery of proteins has, until recently, been difficult to achieve, due primarily to the bioavailability barrier of the plasma membrane. During the past 15 years, a variety of peptides called protein transduction domains (PTDs) or cell penetrating peptides (CPPs), have been characterized for their ability to translocate into live cells. The most commonly studied are homeodomain transcription factors such as Antennapedia, the herpes simplex virus (HSV) type 1 protein VP22, and the human immunodeficiency virus (HIV-1) transactivator TAT protein. Recently, polyarginine exhibits even greater efficiency in terms of delivery of several peptides and proteins. Numerous examples of biologically active full-length proteins and peptides have been delivered to cells and tissues, both in vitro and in vivo. These studies offer new avenues for treatment of several diseases. The main mechanism of protein transduction is an electrostatic interaction with the plasma membrane, penetration into cells by macropinocytosis, and a release to cytoplasm and nuclei by retrograde transport. Moreover, the intercellular transfer of endogenous transcription factors, such as TAT and homeoproteins, seems to point to an original and important mode of signal transduction. The protein transduction systems have opened up several possibilities, not only for the development of new peptide/protein drugs but also for consideration of their physiological and developmental implications.</p