科研之友
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摘要
If f(z) is a weight k is an element of 1/2Z meromorphic modular form on Gamma(0)(N) satisfying
f(z) = Sigma(n >= n0) a(n)e(2 pi imnz)
where m inverted iota N, then f is constant. If k not equal 0, then f = 0. Atkin and Lehner [2] derived the theory of integer weight newforms from this fact. We use the geometric theory of modular forms to prove the analog of this fact for modular forms modulo a"". We show that the same conclusion holds if gcd(N l, m) = 1 and the nebentypus character is trivial at l. We use this to study the parity of the partition function and the coefficients of Klein's j-function.
- 出版日期2012-1
