# 佐賀大学理工学部第185回応数談話会

## 談話会

２００６年２月１６日（木）１６：１０〜１７：１０

Waring's problem for polytope numbers

The sum of four squares (SFS), which was proved by Lagrange in 1770, states that every natural number can be written as a sum of four squares. The theme of this talk is various generalizations of this beautiful result. There are two classical generalizations of Lagrange's SFS. The one is Cauchy's polygonal number theorem which can be viewed as a horizontal generalization of the SFS, and the other is Waring's problem which can be viewed as a higher dimensional generalization of the SFS. As further generalizations, we introduce two types of Waring's problem, namely Waring's problem for integer valued polynomials (an arithmetic generalization) and Waring's problem for polytope numbers (a geometric generalization). We next introduce the circle method which was initiated by Hardy and Littlewood in 1920's. We will use the circle method to illustrate that Waring's problem for polytope numbers is more natural than that for integer valued polynomials.

〒840-8502 佐賀市本庄町1 佐賀大学理工学部数理科学科

TEL 0952-28-8521 　FAX 0952-28-8501

## 大学院集中講義(応用離散数理（専攻外科目）)

２００６年２月１７日（金）〜２月２１日（火）

```校時　金　I, II, III, IV
土　I, II, III, IV
月　I, II, III, IV
火  I, II, III

(担当校時の割り振りは予定)
I校時 金　賢光（Kim Hyun kwang）
II校時 上原　健
III校時 中原　徹
IV校時 演習
```