منابع مشابه
Differentiation Evens out Zero Spacings
Abstract. Suppose f(x) is a polynomial with all of its roots on the real line. We show that the roots of f (x) are more evenly spaced than the roots of f(x). The same holds for polynomials with all their zeros on a circle, as well as an entire function of order 1 with all its zeros on a line. Applications are given to the Riemann zeta-function and its connection to random matrix polynomials. We...
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Partitions with no repeated even parts (DE-partitions) are considered. A DE-rank for DE-partitions is defined to be the integer part of half the largest part minus the number of even parts. ∆(n) denotes the excess of the number of DE-partitions with even DE-rank over those with odd DE-rank. Surprisingly ∆(n) is (1) always non-negative, (2) almost always zero, and (3) assumes every positive inte...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03721-9