Determination of the algebraic relations among special Gamma-values in positive characteristic

Algebraic independence of arithmetic gamma values and Carlitz zeta values

We consider the values at proper fractions of the arithmetic gamma function and the values at positive integers of the zeta function for F_q[theta] and provide complete algebraic independence results for them.

Fractal algebraic and linguistic structures generated by the Laurent series for the Gamma function near its negative poles

We give closed-form expressions for the Laurent series coefficients of the Gamma function near all its strictly negative singularities. These closed-form expressions are clearly self-similar. We briefly describe their algebraic and grammatical budding patterns. As the degree of the coefficient grows to infinity its global structure becomes a fractal.

On determination of periods of geometric continued fractions for two-dimensional algebraic hyperbolic operators

For a given sequence of positive integers we make an explicit construction of a reduced hyperbolic operator in SL(2,z) with the sequence as a period of a geometric continued fraction in the sense of Klein. Further we experimentally study an algorithm to construct a period for an arbitrary operator of SL(2,z) (the Gauss Reduction Theory).

The p-adic closure of a subgroup of rational points on a commutative algebraic group

Let G be a commutative algebraic group over Q. Let Gamma be a subgroup of G(Q) contained in the union of the compact subgroups of G(Q_p). We formulate a guess for the dimension of the closure of Gamma in G(Q_p), and show that its correctness for certain tori is equivalent to Leopoldt's conjecture.

特殊伽马值之间的代数关系及函数域上的丘-塞尔伯格现象

Algebraic Relations among Special Gamma Values and the Chowla-Selberg Phenomenon over Function Fields

本文研究了函数域上特殊伽马值的代数关系，并证明了CM阿贝尔$t$-模准周期的丘-塞尔伯格型公式。

On the algebraicity of some products of special values of Barnes' multiple gamma function

We consider partial zeta functions $ζ(s,c)$ associated with ray classes $c$'s of a totally real field. Stark's conjecture implies that an appropriate product of $\exp(ζ'(0,c))$'s is an algebraic number which is called a Stark unit. Shintani gave an explicit formula for $\exp(ζ'(0,c))$ in terms of Barnes' multiple gamma function. Yoshida ``decomposed'' Shintani's formula: he defined the symbol $X(c,ι)$ satisfying that $\exp(ζ'(0,c))=\prod_ι \exp(X(c,ι))$ where $ι$ runs over all real embeddings of $F$. Hence we can decompose a Stark unit into a product of $[F:\mathbb Q]$ terms. The main result i…