Hilbert Poincaré级数与$L$ -函数乘积的核
Hilbert Poincaré series and kernels for products of $L$-functions
摘要：
研究了与一般种子函数相联系的Hilbert Poincaré级数，构造了Cohen核和双Eisenstein级数作为Hilbert Poincaré级数的级数.然后计算了Hilbert Poincaré级数和Hilbert模形式的Rankin-Cohen括号，并将Zagier核公式推广到全实数域.最后，我们证明了两种不同类型的Eisenstein级数的Rankin-Cohen括号是二重Eisenstein级数直到常数的特殊值。
英文摘要：
We study Hilbert Poincaré series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincaré series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincaré series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant.
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