Let \(\Gamma \) be a geometrically finite Fuchsian group and suppose that \(\chi :\Gamma \rightarrow {{\,\mathrm{GL}\,}}(V)\) is a finite-dimensional representation with non-expanding cusp monodromy. We show that the parabolic Eisenstein series for \(\Gamma \) with twist \(\chi \) converges on some half-plane. Further, we develop Fourier-type expansions for these Eisenstein series.

中文翻译：

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爱森斯坦（Eisenstein）系列扭曲了非膨胀的尖端单斜体

令\（\ Gamma \）为几何有限的Fuchsian群，并假设\（\ chi：\ Gamma \ rightarrow {{\，\ mathrm {GL} \，}}（V）\）是具有以下项的有限维表示不扩张的尖尖单峰。我们证明，具有扭曲\（\ chi \）的\（\ Gamma \）的抛物线Eisenstein级数收敛于某个半平面。此外，我们为这些爱森斯坦级数开发了傅立叶型展开。