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A construction of p-adic Asai L-functions for \(\mathrm{GL}_2\) over CM fields


We give a construction of p-adic Asai L-functions for cohomological cuspidal automorphic representations of \(\mathrm{GL}_2\) over CM fields. If the base field is imaginary quadratic, Loeffler–Williams recently constructed such p-adic Asai L-functions. We generalize their construction to the case that the base fields are general CM fields.

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The author is sincerely grateful to Ming-Lun Hsieh. The discussion with him on this subject was very helpful for preparing this paper. The author also thanks to David Loeffler for pointing out the paper [4] and his comments. The paper is indebted to Tadashi Ochiai for his valuable suggestions. The author is grateful to the referee for suggestions on the improvement of the present paper.

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Correspondence to Kenichi Namikawa.

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The author was supported by JSPS Grant-in-Aid for Young Scientists (B) Grand No. JP17K14174 and JSPS Grant-in-Aid for Scientific Research (C) Grand No. JP21K03207.

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Namikawa, K. A construction of p-adic Asai L-functions for \(\mathrm{GL}_2\) over CM fields. manuscripta math. (2021).

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Mathematics Subject Classification

  • 11F67
  • 11F75
  • 11R23