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Vector-Valued Modular Forms on Finite Upper Half Planes

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Arithmetic of Finite Fields (WAIFI 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11321))

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Abstract

Finite upper half planes are finite field analogs of the Poincaré upper half plane. Vector-valued modular forms on finite upper half planes are introduced, and then equivariant functions on these planes are defined. The existence of these functions is an application of vector-valued modular forms.

Supported by JSPS KAKENHI Grant Number 15K04801.

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Acknowledgments

The author would like to thank the anonymous referees for careful reading and insightful comments that improved this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Okayama University of Science, Ridai-cho 1-1, Okayama, 700-0005, Japan

    Yoshinori Hamahata

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  1. Yoshinori Hamahata
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Correspondence to Yoshinori Hamahata .

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Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Lilya Budaghyan

  2. Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Mexico, Mexico

    Francisco Rodríguez-Henríquez

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Hamahata, Y. (2018). Vector-Valued Modular Forms on Finite Upper Half Planes. In: Budaghyan, L., Rodríguez-Henríquez, F. (eds) Arithmetic of Finite Fields. WAIFI 2018. Lecture Notes in Computer Science(), vol 11321. Springer, Cham. https://doi.org/10.1007/978-3-030-05153-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-05153-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-05152-5

  • Online ISBN: 978-3-030-05153-2

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