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3 results

  • ON η3(aτ)η3(bτ) WITH a+b=8

  • Part of
  • HENG HUAT CHAN, SHAUN COOPER, WEN-CHIN LIAW
  • Journal:
    Journal of the Australian Mathematical Society / Volume 84 / Issue 3 / June 2008
    Published online by Cambridge University Press:
    01 June 2008, pp. 301-313
    Print publication:
    June 2008
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  • Weprove an observation associated with η3(τ)η3(7τ) whichis found on page 54 of Ramanujan’s Lost Notebook (S. Ramanujan, The Lost Notebook and Other Unpublished Papers (Narosa, New Delhi, 1988)). We then study functions of the type η3(aτ)η3(bτ) with a+b=8.

  • On Russell-Type Modular Equations

  • Heng Huat Chan, Wen-Chin Liaw
  • Journal:
    Canadian Journal of Mathematics / Volume 52 / Issue 1 / 01 February 2000
    Published online by Cambridge University Press:
    20 November 2018, pp. 31-46
    Print publication:
    01 February 2000
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  • In this paper, we revisit Russell-type modular equations, a collection of modular equations first studied systematically by R. Russell in 1887. We give a proof of Russell’s main theorem and indicate the relations between such equations and the constructions of Hilbert class fields of imaginary quadratic fields. Motivated by Russell’s theorem, we state and prove its cubic analogue which allows us to construct Russell-type modular equations in the theory of signature 3.