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<p>Jacobi theta functions with rational characteristics can be viewed as vector-valued Jacobi forms. Theta relations usually correspond to different constructions of certain Jacobi forms. From this observation, we extract a new approach, which is called orbits of Jacobi forms, to produce identities on Jacobi theta functions. Our approach not only provides simple proofs of many known theta relations but also produces a large number of new identities, which can be considered as generalizations of Riemann’s theta relations.</p>

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Orbits of Jacobi forms and theta relations

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Valery Gritsenko,
  • Haowu Wang

摘要

Jacobi theta functions with rational characteristics can be viewed as vector-valued Jacobi forms. Theta relations usually correspond to different constructions of certain Jacobi forms. From this observation, we extract a new approach, which is called orbits of Jacobi forms, to produce identities on Jacobi theta functions. Our approach not only provides simple proofs of many known theta relations but also produces a large number of new identities, which can be considered as generalizations of Riemann’s theta relations.