An explicit formula of the normalized Mumford form

英文摘要：

We give an explicit formula of the normalized Mumford form which expresses the second tautological line bundle by the Hodge line bundle defined on the moduli space of algebraic curves of any genus. This formula is represented by an infinite product which is a higher genus version of the Ramanujan delta function under the trivialization by normalized abelian differentials and Eichler integrals of their products. By this formula, we have a universal expression of the normalized Mumford form as a computable power series with integral coefficients by the moduli parameters of algebraic curves.