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  2. Ramanujan–Petersson conjecture - Wikipedia

    en.wikipedia.org/wiki/Ramanujan–Petersson...

    The more general Ramanujan–Petersson conjecture for holomorphic cusp forms in the theory of elliptic modular forms for congruence subgroups has a similar formulation, with exponent (k − 1)/2 where k is the weight of the form.

  3. Ramanujan–Sato series - Wikipedia

    en.wikipedia.org/wiki/Ramanujan–Sato_series

    In mathematics, a Ramanujan–Sato series [1] [2] generalizes Ramanujan’s pi formulas such as, = = ()!! + to the form = = + by using other well-defined sequences of integers obeying a certain recurrence relation, sequences which may be expressed in terms of binomial coefficients (), and ,, employing modular forms of higher levels.

  4. Mock modular form - Wikipedia

    en.wikipedia.org/wiki/Mock_modular_form

    In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight ⁠ 1 / 2 ⁠. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook .

  5. Ramanujan's congruences - Wikipedia

    en.wikipedia.org/wiki/Ramanujan's_congruences

    The web of modularity: arithmetic of the coefficients of modular forms and q-series. CBMS Regional Conference Series in Mathematics. Vol. 102. Providence, RI: American Mathematical Society. ISBN 978-0-8218-3368-1. Zbl 1119.11026. Ramanujan, S. (1919). "Some properties of p(n), the number of partitions of n".

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    Some forms of city directories provide this form of lookup for listed services by phone number, along with address cross-referencing. Publicly accessible reverse telephone directories may be provided as part of the standard directory services from the telecommunications carrier in some countries.

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  9. Cusp form - Wikipedia

    en.wikipedia.org/wiki/Cusp_form

    For example, the Ramanujan tau function τ(n) arises as the sequence of Fourier coefficients of the cusp form of weight 12 for the modular group, with a 1 = 1. The space of such forms has dimension 1, which means this definition is possible; and that accounts for the action of Hecke operators on the space being by scalar multiplication (Mordell ...

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