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Modularity of Asymptotically Optimal Towers of Function Fields

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Coding, Cryptography and Combinatorics

Part of the book series: Progress in Computer Science and Applied Logic ((PCS,volume 23))

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Abstract

Elkies conjectures that all recursively defined asymptotically optimal towers of function fields over finite fields with square cardinality arise from elliptic modular curves, Shimura curves, or Drinfeld modular curves by appropriate reduction. In this paper we review the recursive asymptotically optimal towers constructed so far, discuss the reasons behind Elkies’ conjecture, present numerical evidence of this conjecture, and sketch Elkies’ proof of modularity of the new families.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, 16802, University Park, PA, USA

    Wen-Ching Winnie Li

Authors
  1. Wen-Ching Winnie Li
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Keqin Feng

  2. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter  & Chaoping Xing  & 

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Li, WC.W. (2004). Modularity of Asymptotically Optimal Towers of Function Fields. In: Feng, K., Niederreiter, H., Xing, C. (eds) Coding, Cryptography and Combinatorics. Progress in Computer Science and Applied Logic, vol 23. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7865-4_3

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  • DOI: https://doi.org/10.1007/978-3-0348-7865-4_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9602-3

  • Online ISBN: 978-3-0348-7865-4

  • eBook Packages: Springer Book Archive

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