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Number Theory pp 287–300Cite as

Birkhäuser

Algebraic Curves Over Finite Fields with many Rational Points and their Applications

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Part of the book series: Trends in Mathematics ((TM))

Abstract

Algebraic curves over finite fields with many rational points have received a lot of attention in recent years. We present a survey of this subject covering both the case of fixed genus and the asymptotic theory. A strong impetus in the asymptotic theory has come from a thorough exploitation of the method of infinite class field towers. On the other hand, we show by a counterexample that Perret’s conjecture on infinite class field towers is wrong, and so Perret’s method of infinite ramified class field towers breaks down. In the last two sections of the paper we discuss applications of algebraic curves over finite fields with many rational points to coding theory and to the construction of low-discrepancy sequences.

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Author information

Authors and Affiliations

  1. Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010, Vienna, Austria

    Harald Niederreiter

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

    Chaoping Xing

Authors
  1. Harald Niederreiter
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  2. Chaoping Xing
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Editor information

Editors and Affiliations

  1. Centre for Advanced Study in Mathematics, Panjab University, 160 012, Chandigarh, India

    R. P. Bambah , V. C. Dumir  & R. J. Hans-Gill ,  & 

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© 2000 Hindustan Book Agency (India) and Indian National Science Academy

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Niederreiter, H., Xing, C. (2000). Algebraic Curves Over Finite Fields with many Rational Points and their Applications. In: Bambah, R.P., Dumir, V.C., Hans-Gill, R.J. (eds) Number Theory. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7023-8_15

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  • DOI: https://doi.org/10.1007/978-3-0348-7023-8_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-7025-2

  • Online ISBN: 978-3-0348-7023-8

  • eBook Packages: Springer Book Archive

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