The Ramanujan Journal

, Volume 10, Issue 1, pp 43–50 | Cite as

Congruences Concerning Values of the Modular Functions j n



The j-function j(z) = q−1+ 744 + 196884q + ⋅s plays an important role in many problems. In [7], Zagier, presented an interesting series of functions obtained from the j-function: j m (ζ) = (j(ζ) – 744)∨T0(m), where T0(m) is the usual m′th normalized weight 0 Hecke operator. In [3], Bruinier et al. show how this series of functions can be used to describe all meromorphic modular forms on SL2(ℤ). In this note we use these functions and basic notions about modular forms to determine previously unidentified congruence relations between the coefficients of Eisenstein series and the j-function.


modular forms Hecke operators j-function σ function 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadison

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