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We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi grou...
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, whi...
We analyse a surprising connection between Bak--Sneppen type models and much simpler Markov processes, which we call rank-driven processes (RDPs).
The Rank and the Crank Modulo 5     Crank Modulo 5  Rank       2010/3/5
Let p(n) denote the number of partitions of n . Ramanujan's partition congruences are p(5n + 4) , p(7n + 5) and p(11n + 6) = mod 5, 7, and 11, respectively. These have been proved in number of ways. ...

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