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  2. Ramanujan–Petersson conjecture - Wikipedia

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

    Furthermore, we can concretely calculate the dimension of the space of holomorphic modular forms, using the Riemann–Roch theorem (see the dimensions of modular forms). Deligne (1971) used the Eichler–Shimura isomorphism to reduce the Ramanujan conjecture to the Weil conjectures that he later proved.

  3. 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 .

  4. Ramanujan tau function - Wikipedia

    en.wikipedia.org/wiki/Ramanujan_tau_function

    Ramanujan (1916) observed, but did not prove, the following three properties of τ(n): τ(mn) = τ(m)τ(n) if gcd(m,n) = 1 (meaning that τ(n) is a multiplicative function); τ(p r + 1) = τ(p)τ(p r) − p 11 τ(p r − 1) for p prime and r > 0.

  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".

  6. Add, edit, or delete Address Book contacts in AOL Desktop Gold

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    The Address Book in Desktop Gold helps you keep track of email addresses, phone numbers, mailing addresses, birthdays, and anniversaries of your contacts. You can sort your Address Book by last name, first name, email address, screen name, telephone number, or category. Just use the Quick Find box to easily search through your contacts. Add a ...

  7. 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.

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    Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!

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