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arXiv · 1801.05562

An Explicit CM Type Norm Formula and Effective Nonvanishing of Class Group L-functions for CM Fields

Liyang Yang
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Abstract

We show that the central value of class group L-functions of CM fields can be expressed in terms of derivatives of real-analytic Hilbert Eisenstein series at CM points. Then, following an idea of Iwaniec and Kowalski we obtain a conditional explicit lower bound of class numbers of CM fields under a weaker assumption. Some results in the proof lead to an effective nonvanishing result for class group L-functions of general CM fields, generalizing the only known ineffective results.

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Liyang Yang. 2018-01-17. An Explicit CM Type Norm Formula and Effective Nonvanishing of Class Group L-functions for CM Fields. https://arxiv.org/abs/1801.05562

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