Ramanujan's unpublished manuscript on the partition and tau functions with proofs and commentary
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Publication:1290729
zbMath0932.11002MaRDI QIDQ1290729
Publication date: 16 June 1999
Published in: Séminaire Lotharingien de Combinatoire (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/120145
History of mathematics in the 20th century (01A60) Partitions; congruences and congruential restrictions (11P83) Research exposition (monographs, survey articles) pertaining to number theory (11-02) History of number theory (11-03) Holomorphic modular forms of integral weight (11F11) Analytic theory of partitions (11P82)
Related Items (27)
Variations of Lehmer's conjecture for Ramanujan's tau-function ⋮ On eight colour partitions ⋮ Ramanujan’s Elementary Method in Partition Congruences ⋮ Even values of Ramanujan's tau-function ⋮ Identities and congruences for the general partition and Ramanujan's tau functions ⋮ Ramanujan-type systems of nonlinear ODEs for \(\Gamma_0 (2)\) and \(\Gamma_0 (3)\) ⋮ Scarcity of congruences for the partition function ⋮ Variants of Lehmer's speculation for newforms ⋮ A CONJECTURE OF MERCA ON CONGRUENCES MODULO POWERS OF 2 FOR PARTITIONS INTO DISTINCT PARTS ⋮ Theorems on partitions from a page in Ramanujan's lost notebook ⋮ A theory of theta functions to the quintic base ⋮ On the gaps in the Fourier expansion of cusp forms ⋮ Values of the Euler 𝜙-function not divisible by a given odd prime, and the distribution of Euler-Kronecker constants for cyclotomic fields ⋮ Congruences of multipartition functions modulo powers of primes ⋮ Congruences for a certain partition function ⋮ Congruences modulo \(p^2\) and \(p^3\) for \(k\) dots bracelet partitions with \(k = m p^s\) ⋮ Congruences modulo powers of 2 for a certain partition function ⋮ Ramanujan's ``lost notebook and the Virasoro algebra ⋮ Partition function congruences: Some flowers and seeds from `Ramanujan's Garden' ⋮ Chebyshev’s bias for composite numbers with restricted prime divisors ⋮ The hexagonal versus the square lattice ⋮ An algebraic independence result for Euler products of finite degree ⋮ Congruence properties of pk(n) ⋮ Proof of a conjecture by Ahlgren and Ono on the non-existence of certain partition congruences ⋮ Landau and Ramanujan approximations for divisor sums and coefficients of cusp forms ⋮ On the Shimura lift modulo 2 ⋮ EXTREMAL QUASIMODULAR FORMS OF LOWER DEPTH WITH INTEGRAL FOURIER COEFFICIENTS
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