Partition Polynomials: Asymptotics and Zeros
نویسندگان
چکیده
Let Fn(x) be the partition polynomial ∑k=1 pk(n)x where pk(n) is the number of partitions of n with k parts. We emphasize the computational experiments using degrees up to 70,000 to discover the asymptotics of these polynomials. Surprisingly, the asymptotics of Fn(x) have two scales of orders n and √ n and in three different regimes inside the unit disk. Consequently, the zeros converge to network of curves inside the unit disk given in terms of the dilogarithm.
منابع مشابه
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