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Proceedings of the London Mathematical Society Advance Access published online on April 25, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdn006
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© 2008 London Mathematical Society

Minimal vanishing sums of roots of unity with large coefficients

John P. Steinberger

Received 26 April 2007. Revision received 27 July 2007.

A vanishing sum Formula , where {zeta}n is a primitive nth root of unity and the ais are non-negative integers is called minimal if the coefficient vector (a0, ..., an–1) does not properly dominate the coefficient vector of any other such non-zero sum. We show that for every cisinN there is a minimal vanishing sum of nth roots of unity with its greatest coefficient equal to c, where n is of the form 3pq for odd primes p, q. This solves an open problem posed by Lenstra Jr.

This research was supported by NSF VIGRE grant DMS-0135345.

2000 Mathematics Subject Classification 11R18.


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