On special values of the multiple zeta functions of Arakawa-Kaneko type
- 2019年3月16日15:00 - 17:30
大野 泰生 (東北大学 理学部数学科 教授)
鈴木 雄太 (名古屋大学 大学院多元数理科学研究科 学振特別研究員)
15:00~16:00: Yasuo Ohno (Tohoku University)
"On special values of the multiple zeta functions of Arakawa-Kaneko type"
Arakawa-Kaneko's zeta function is a kind of generalization of the Riemann zeta function by using polylogarithms. I am planning to introduce two topics on combinatorics around its values at positive or negative integral points. This talk is based on joint work with N. Kawasaki.
16:20~17:20: Yuta Suzuki (Nagoya University)
"On relatively prime amicable pairs"
A famous Greek mathematician, Pythagoras tried to find symbolical meanings in numbers. One famous example of such symbolism in numbers is amicable pair, which was introduced as a symbol of friendship. A pair of positive integers $(M,N)$ is called an amicable pair if the sum of all divisors of $M$ except $M$ itself is equal to $N$ and the sum of all divisors of $M$ except $N$ itself is also equal to $M$. The smallest example is $(220,284)$.
Even amicable numbers are introduced more than 20 centuries ago, most of their properties are still unknown. For example, the infinitude of amicable pairs has not yet been proven. In this talk, we pick up a conjecture of Gmelin (1917), which claims that there is no relatively prime amicable pairs, and try to introduce some atmosphere of "modern elementary number theory". In particular, we improve Pollack's partial result (2015) on Gmelin's conjecture.