Hecke-symmetry and rational period functions

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• 作者：Wendell Ressler
• 关键词：Hecke groups ; Rational period functions ; Binary quadratic forms ; Hecke ; symmetry
• 刊名：The Ramanujan Journal
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：41
• 期：1-3
• 页码：323-334
• 全文大小：413 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Number Theory
  Field Theory and Polynomials
  Combinatorics
  Fourier Analysis
  Functions of a Complex Variable
  
• 出版者：Springer U.S.
• ISSN：1572-9303
• 卷排序：41

文摘

In this paper, we continue our work in the direction of a characterization of rational period functions on the Hecke groups. We examine the role that Hecke-symmetry of poles plays in this setting, and pay particular attention to non-symmetric irreducible systems of poles for a rational period function. This gives us a new expression for a class of rational period functions of any positive even integer weight on the Hecke groups. We illustrate these properties with examples of specific rational period functions. We also correct the wording of a theorem from an earlier paper.