Analogues of Ramanujan's 24 squares formula

作者：Uygul Faruk^*; Williams Kenneth S

来源：International Journal of Number Theory, 2014, 10(5): 1099-1119.

DOI：10.1142/S1793042114500171

• Ramanujan's 24 squares formula
• sums of squares and triangular numbers
• Ramanujan's tau function
• sum of divisors function
• Eisenstein series
• infinite products
• Dedekind eta function
• modular forms

Ramanujan's formula for the number r(24)(n) of representations of a positive integer n as a sum of 24 squares asserts that
[GRAPHICS]
,
where
[GRAPHICS]
and Ramanujan's function tau(n) is given by
q pi(infinity)(n=1) (1-q(n))(24) = Sigma(infinity)(n=1) tau(n)q(n), q is an element of C, |q| < 1.
In this paper, we determine a class of formulae analogous to Ramanujan's formula for r(24()n).

• 出版日期2014-8