Kaneko–Zagier type equation for Jacobi forms of index 1

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• 作者：Tomoya Kiyuna
• 关键词：Jacobi forms ; Differential operators ; 11F50 ; 11F60
• 刊名：The Ramanujan Journal
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：39
• 期：2
• 页码：347-362
• 全文大小：441 KB
• 参考文献：1.Dabholkar, A., Murthy, S., Zagier, D.: Quantum black holes, wall crossing, and mock modular forms. Cambridge Monographs in Mathematical Physics (2012, to appear)
  2.Eichler, M., Zagier, D.: The Theory of Jacobi Forms, Birkhäuser, Boston (1985)
  3.Guerzhoy, P.: A mixed mock modular solution of the Kaneko–Zagier equation. Ramanujan J (2013). doi:10.​1007/​s11139-013-9496-9
  4.Ibukiyama, T.: Vector valued Siegel modular forms of symmetric tensor weight of small degrees. Comment. Math. Univ. St. Pauli. 61, 51–75 (2012)
  5.Kaneko, M., Koike, M.: On modular forms arising from a differential equation of hypergeometric type. Ramanujan J. 7, 145–164 (2003)MATH MathSciNet CrossRef
  6.Kaneko, M., Nagatomo, K., Sakai, Y.: Modular forms and second order ordinary differential equations: applications to vertex operator algebras. Lett. Math. Phys. 103(4), 439–453 (2013)MATH MathSciNet CrossRef
  7.Kaneko, M., Zagier, D.: Supersingular j-invariants, hypergeometric series, and Atkin’s orthogonal polynomials. AMS/IP Stud. Adv. Math. 7, 97–126 (1998)MathSciNet
  8.Richter, O.: The action of the heat operator on Jacobi forms. Proc. Amer. Math. Soc. 137, 869–875 (2009)MATH MathSciNet CrossRef
  
• 作者单位：Tomoya Kiyuna (1)
  
  1. Graduate School of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
  
• 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

文摘

We introduce a certain fourth-order partial differential equation containing one parameter \(k\), related to Jacobi forms of index 1. We show several properties of the equation and give explicit Jacobi-form solutions for suitable \(k\). Keywords Jacobi forms Differential operators