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Indecomposable vector-valued modular forms and periods of modular curves

  • Luca Candelori
  • Tucker Hartland
  • Christopher Marks
  • Diego Yépez
Research

Abstract

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be employed to compute periods of modular curves. This technique obviates the use of Hecke operators, and therefore provides a method for studying noncongruence modular curves as well as congruence.

Keywords

Indecomposable representations Modular forms Periods 

Mathematics Subject Classification

11F12 11F23 

Notes

Acknowledgements

We would like to acknowledge Bill Hoffman, Ling Long and Geoff Mason for helpful discussions. The first author would like to thank the Mathematics Department at Chico State for the hospitality enjoyed during the brief visit in which this article was initiated. We would also like to thank the referees for numerous comments and a correction to an earlier version of the manuscript.

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Copyright information

© SpringerNature 2018

Authors and Affiliations

  • Luca Candelori
    • 1
  • Tucker Hartland
    • 2
  • Christopher Marks
    • 3
  • Diego Yépez
    • 4
  1. 1.Department of MathematicsUniversity of HawaiiHonoluluUSA
  2. 2.Department of Applied MathematicsUniversity of California, MercedMercedUSA
  3. 3.Department of Mathematics and StatisticsCalifornia State University, ChicoChicoUSA
  4. 4.School of Engineering and Computer ScienceUniversity of the PacificStocktonUSA

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