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Second-Order Modular Forms with Characters

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Part of the book series: Developments in Mathematics ((DEVM,volume 28))

Abstract

We introduce spaces of second-order modular forms for which the relevant action involves characters. We compute the dimensions of these spaces by constructing explicit bases.

Mathematics Subject Classification (2010): 11F, 60K35

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References

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Acknowledgements

We thank Peter Kleban for several interesting comments and the referee for a very careful reading of the manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Thomas Blann & Nikolaos Diamantis

Authors
  1. Thomas Blann
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  2. Nikolaos Diamantis
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Corresponding author

Correspondence to Nikolaos Diamantis .

Editor information

Editors and Affiliations

  1. , Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Hershel M. Farkas

  2. , Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, 08544, New Jersey, USA

    Robert C. Gunning

  3. , Department of Mathematics, Temple University, Wachman Hall 608, Philadelphia, 19122, Pennsylvania, USA

    Marvin I. Knopp

  4. , Department of Mathematics, University of Michigan, Church St. 530, Ann Arbor, 48109, Michigan, USA

    B. A. Taylor

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Dedicated to the memory of Leon Ehrenpreis

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Blann, T., Diamantis, N. (2013). Second-Order Modular Forms with Characters. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_4

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