A basis for S (k) (I%26quot; (0)(4)) and representations of integers as sums of squares

作者：Fukuhara Shinji; Yang Yifan^*

来源：Ramanujan Journal, 2012, 28(1): 25-43.

DOI：10.1007/s11139-011-9341-y

• Modular forms (one variable)
• Period polynomials
• Fourier coefficients of modular forms
• Sum of squares

In this paper, we find a basis for the space S (k) (I%26quot; (0)(4)) of cusp forms of even weight k for the congruence subgroup I%26quot; (0)(4) in terms of Eisenstein series. As an application, we obtain formulas for r (4s) (n), the number of ways to represent a nonnegative integer n as a sum of 4s integral squares.

• 出版日期2012-5