Knot invariants, modular forms and elliptic Dedekind sums

我们工作的特点是研究Dedekind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很好的基，这是很重要的一步。我们也得到了用爱森斯坦级数表示幂的公式。这些公式给出了整数的平方和的表示形式。从数论和几何的角度来看，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.