Lecture Room B, 4th Floor, The 3rd General Building, NTHU

(清華大學綜合三館 4樓B演講室)

Transcendence of v-adic Carlitz Multiple Star Polylogarithms at Algebraic Points

Yoshinori Mishiba (University of the Ryukyus)

Abstract:

Carlitz multiple star polylogarithms (CMSPL's) are generalizations of the logarithmic function of the Carlitz t-module. In the infinite-adic case, Chang proved that all nonzero infinite-adic CMSPL's at algebraic points are transcendental in 2014. In this talk, I will consider a v-adic analogue of this result, where v is a finite place of a function field. In particular, I will show that v-adic CMSPL's at certain algebraic points are transcendental. Note that the depth one case was essentially proved by Yu in 1991. The key idea of the proof is logarithmic interpretations of CMSPL's. We then apply v-adic transcendence theory of Yu to achieve the desired result.