论文标题
局部和谐的玛刺形式和杂形模块化的时期
Locally harmonic Maass forms and periods of meromorphic modular forms
论文作者
论文摘要
我们研究了一个与模块化形式时期相对应的局部谐波形式的新家族。它们像负重模块化形式一样变化，除了无限的大地测量界跳跃奇异点外，它们是谐波的。我们的主要结果是将新的局部和谐玛刺形式明确分为谐波部分和捕获跳跃奇点的本地多项式部分。作为一种应用，我们获得了有限的合理公式，以适用于与阳性确定二进制二元形式相关的Meromormormormormormormormormormormormormormormorormormorormormormormorormorthic组合的线性组合。
We investigate a new family of locally harmonic Maass forms which correspond to periods of modular forms. They transform like negative weight modular forms and are harmonic apart from jump singularities along infinite geodesics. Our main result is an explicit splitting of the new locally harmonic Maass forms into a harmonic part and a locally polynomial part that captures the jump singularities. As an application, we obtain finite rational formulas for suitable linear combinations of periods of meromorphic modular forms associated to positive definite binary quadratic forms.
