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On the Partial Sums of the Rearrangements of a Complex Series
Author(s) -
Kleitman D. J.,
Li Shuo-Yen Robert
Publication year - 1981
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1981642177
Subject(s) - magnitude (astronomy) , series (stratigraphy) , mathematics , combinatorics , set (abstract data type) , upper and lower bounds , mathematical analysis , physics , computer science , astrophysics , geology , paleontology , programming language
Let { z j } be a set of complex numbers, all with magnitude ⩽ 1, which sum to a real number ε⩾1. Then the z j 's can be rearranged so that all partial sums are no greater in magnitude than (ε 2 + 1) 1/2 , and this bound is best possible. Bergström showed that if , the best bound is .