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Hamiltonians arising from L-functions in the Selberg class
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-06-10 , DOI: 10.1016/j.jfa.2021.109116 Masatoshi Suzuki
中文翻译:
由Selberg 类中的L函数产生的哈密顿量
更新日期:2021-06-17
Journal of Functional Analysis ( IF 1.7 ) Pub Date : 2021-06-10 , DOI: 10.1016/j.jfa.2021.109116 Masatoshi Suzuki
We establish a new equivalent condition for the Grand Riemann Hypothesis for L-functions in a wide subclass of the Selberg class in terms of canonical systems of differential equations. A canonical system is determined by a real symmetric matrix-valued function called a Hamiltonian. To establish the equivalent condition, we use an inverse problem for canonical systems of a special type.
中文翻译:
由Selberg 类中的L函数产生的哈密顿量
我们根据微分方程的规范系统为 Selberg 类的一个广泛子类中的L函数的 Grand Riemann 假设建立了一个新的等价条件。典型系统由称为哈密顿量的实对称矩阵值函数确定。为了建立等效条件,我们对特殊类型的规范系统使用逆问题。