Modular Symbols have a Normal Distribution
Modular Symbols have a Normal Distribution
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模符号服从正态分布
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Morten S. Risager
中科院分区：
文献类型：
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作者：
Y. Petridis;Morten S. Risager
摘要：我们证明了适当规范化和有序化的模符号对所有余有限子群都有高斯分布，
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$${\text{SL}}_{\text{2}}（\mathbb{R}）.$$利用谱变形研究了模符号幂扭曲的爱森斯坦级数的极点和剩余。
Abstract.We prove that the modular symbols appropriately normalized and ordered have a Gaussian distribution for all cofinite subgroups of
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$${\text{SL}}_{\text{2}} (\mathbb{R}).$$ We use spectral deformations to study the poles and the residues of Eisenstein series twisted by power of modular symbols.