A note on Dedekind zeta values at 1/2

For a number field [Formula: see text], let [Formula: see text] be the Dedekind zeta function associated to [Formula: see text]. In this paper, we study non-vanishing and transcendence of [Formula: see text] as well as its derivative [Formula: see text] at [Formula: see text]. En route, we strengthen a result proved by Ram Murty and Tanabe [On the nature of [Formula: see text] and non-vanishing of [Formula: see text]-series at [Formula: see text], J. Number Theory 161 (2016) 444–456].

Analytic properties of Ohno function

Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute convergence, give some new expressions, and show new relations of the function. We also give a direct proof of the interpolation of Ohno's relation.

Non-vanishing of certain cyclotomic multiple harmonic sums and application to the non-vanishing of certain p-adic cyclotomic multiple zeta values

We define and apply a method to study the non-vanishing of [Formula: see text]-adic cyclotomic multiple zeta values. We prove the non-vanishing of certain cyclotomic multiple harmonic sums, and, via a formula proved in another paper, which expresses certain cyclotomic multiple harmonic sums as infinite sums of products of [Formula: see text]-adic cyclotomic multiple zeta values, this implies the non-vanishing of certain [Formula: see text]-adic cyclotomic multiple zeta values.

Zero distribution of v-adic multiple zeta values over 𝔽q(t)

This paper aims to study the zero distribution of [Formula: see text]-adic multiple zeta values over function fields. We show that the interpolated [Formula: see text]-adic MZVs at negative integers only vanish at what we call the “trivial zeros”, for degree one finite place over rational function fields. And we conjecture that this result can be generalized to all finite places.