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Kernels for products of Hilbert L-functions

Abstract

We study kernel functions of L-functions and products of L-functions of Hilbert cusp forms over real quadratic fields. This extends the results on elliptic modular forms in Diamantis and O’Sullivan (Math Ann 346(4):897–929, 2010, Algebra Number Theory 7(8):1883–1917, 2013).

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Acknowledgements

The first author was supported by NRF2018R1A4A1023 590 and NRF2017R1A2B2001807. The second author was partially supported by by HIT Youth Talent Start-Up Grant and Grant of Technology Division of Harbin (RC2016XK001001). We thank the referee for the valuable remarks, which led to improvements in the paper.

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Correspondence to YoungJu Choie.

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Choie, Y., Zhang, Y. Kernels for products of Hilbert L-functions. Math. Z. 295, 87–99 (2020). https://doi.org/10.1007/s00209-019-02355-0

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Keywords

  • Hilbert modular form
  • Special L-values
  • Cusp form
  • Double Eisenstein series
  • Petersson inner product
  • Rankin–Cohen bracket
  • Kernel function

Mathematics Subject Classification

  • Primary 11F67
  • 11F41
  • Secondary 11F03