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On linear relations for L-values over real quadratic fields

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Abstract

In this paper, we give a method to construct a classical modular form from a Hilbert modular form. By applying this method, we can get linear formulas which relate the Fourier coefficients of the Hilbert and classical modular forms. The paper focuses on the Hilbert modular forms over real quadratic fields. We will state a construction of relations between the special values of L-functions, especially at 0, and arithmetic functions. We will also give a relation between the sum of squares functions with underlying fields \(\mathbb {Q}(\sqrt{D})\) and \(\mathbb {Q}\).

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Acknowledgements

The author would like to show his sincere gratitude to Prof. Ikeda for his insight for the main idea of this paper.

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  1. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, Sichuan, China

    Ren-He Su

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  1. Ren-He Su
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Correspondence to Ren-He Su.

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Communicated by Jens Funke.

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Su, RH. On linear relations for L-values over real quadratic fields. Abh. Math. Semin. Univ. Hambg. 88, 317–330 (2018). https://doi.org/10.1007/s12188-018-0199-4

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  • DOI: https://doi.org/10.1007/s12188-018-0199-4

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