论文标题
全态艾森斯坦系列一系列理性权重和伽马功能的特殊值
Holomorphic Eisenstein series of rational weights and special values of Gamma function
论文作者
论文摘要
我们在$γ_0（p）$上提供了所有可能的全体形态Eisenstein系列，其理性权重大于$ 2 $，并且乘数系统与所有cusps的乘数系统相同。我们证明它们是模块化的形式，并提供了傅立叶扩展。我们建立了四种将这种系列等同于理性重量ETA晶状体等同的身份。作为应用程序，我们在任何有理参数中给出了Euler伽马功能的特殊值的串联表达式。这些表达式涉及Dedekind总和的指数总和。
We give all possible holomorphic Eisenstein series on $Γ_0(p)$, of rational weights greater than $2$, and with multiplier systems the same as certain rational-weight eta-quotients at all cusps. We prove they are modular forms and give their Fourier expansions. We establish four sorts of identities that equate such series to rational-weight eta-quotients. As an application, we give series expressions of special values of Euler Gamma function at any rational arguments. These expressions involve exponential sums of Dedekind sums.
