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Showing 1 to 2 of 2 for “"Ramanujan congruences"”.
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Congruences in modular, Jacobi, Siegel, and mock modular forms with applications
We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the …
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Behavior of partition values modulo powers of primes
… of its values lie much deeper. Ninety years ago, Ramanujan proved the celebrated congruences for <italic>p(n)</italic> which bear his name. For example, he proved, for all <italic>n</italic>, that <italic>p(5n + 4) == 0 mod 5</italic>. Work of Ono and others over the last ten years reveals the …