Blar i forfatter Artikler, rapporter og annet (matematikk og statistikk) "Rebák, Örs"

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    • Explicit values for Ramanujan's theta function φ(q) 

      Berndt, Bruce C.; Rebák, Örs (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-01-09)
      This paper provides a survey of particular values of Ramanujan's theta function φ(q) = ∑ q^(n^2), n = −∞ ... ∞, when q = e^(−π√n), where n is a positive rational number. First, descriptions of the tools used to evaluate theta functions are given. Second, classical values are briefly discussed. Third, certain values due to Ramanujan and later authors are given. Fourth, the methods that are used to ...

    • The three missing terms in Ramanujan’s septic theta function identity 

      Rebák, Örs (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-02-23)
      On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for his theta function φ(q): φ(e^{−7π√7}) = 7^{−3/4}φ(e^{−π√7}){1 + ( )^{2/7} + ( )^{2/7} + ( )^{2/7}}. We give the three missing terms. In addition, we calculate the class invariant G_{343} and further special values of φ(e^{−nπ}), for n = 7, 21, 35, and 49.