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  2. Ramanujan tau function - Wikipedia

    en.wikipedia.org/wiki/Ramanujan_tau_function

    The Ramanujan tau function, studied by Ramanujan , is the function : defined ...

  3. Ramanujan–Petersson conjecture - Wikipedia

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

    would have always imaginary roots from many examples. The relationship between roots and coefficients of quadratic equations leads to the third relation, called Ramanujan's conjecture. Moreover, for the Ramanujan tau function, let the roots of the above quadratic equation be α and β, then

  4. Tau function - Wikipedia

    en.wikipedia.org/wiki/Tau_function

    Tau function may refer to: Tau function (integrable systems), in integrable systems; Ramanujan tau function, giving the Fourier coefficients of the Ramanujan modular form; Divisor function, an arithmetic function giving the number of divisors of an integer

  5. Ramanujan's congruences - Wikipedia

    en.wikipedia.org/wiki/Ramanujan's_congruences

    In mathematics, Ramanujan's congruences are the congruences for the partition function p(n) discovered by Srinivasa Ramanujan: ... for numbers and for Tau-functions.

  6. Srinivasa Ramanujan - Wikipedia

    en.wikipedia.org/wiki/Srinivasa_Ramanujan

    Srinivasa Ramanujan Aiyangar [a] (22 December 1887 – 26 April 1920) was an Indian mathematician.Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then ...

  7. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...

  8. Hecke operator - Wikipedia

    en.wikipedia.org/wiki/Hecke_operator

    Mordell () used Hecke operators on modular forms in a paper on the special cusp form of Ramanujan, ahead of the general theory given by Hecke (1937a,1937b).Mordell proved that the Ramanujan tau function, expressing the coefficients of the Ramanujan form,

  9. Wikipedia:Reference desk/Archives/Mathematics/2023 May 24 ...

    en.wikipedia.org/wiki/Wikipedia:Reference_desk/...

    About the prime values of the sigma function and Ramanujan tau function [ edit ] Let σ ( n ) {\displaystyle \sigma (n)} be the sum-of-divisors function (sequence A000203 in the OEIS ) and τ ( n ) {\displaystyle \tau (n)} be the Ramanujan tau function (sequence A000594 in the OEIS ).