Knot invariants, modular forms and elliptic Dedekind sums

我们工作的特点是研究了戴德金符号与模形式的关系。因此，我们为模形式的向量空间构造了良好的基，这是有意义的一步。我们还得到了公式表示的权力的theta函数的爱森斯坦级数。这些公式给我们公式的数目表示整数的平方和。从数论和几何的观点来看，这些似乎很有趣。

The feature of our work is that we study Dedekind symbols in the relation with modular forms. Thus it is a significant step that we have constructed nice bases for the vector spaces of modular forms. We also obtained formulas to express powers of the theta function in terms of Eisenstein series. These formulas give us formulas for the numbers of representations of integers as sums of squares. These seem interesting from number theoretical and geometrical view points.