Waring's number for large subgroups of double-struck Z_p

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dc.contributor.author Cochrane, Todd E.
dc.contributor.author Hart, Derrick
dc.contributor.author Pinner, Christopher G.
dc.contributor.author Spencer, Craig
dc.date.accessioned 2014-11-25T19:08:47Z
dc.date.available 2014-11-25T19:08:47Z
dc.date.issued 2014-11-25
dc.identifier.uri http://hdl.handle.net/2097/18747
dc.description.abstract Let p be a prime, Z_p be the finite field in p elements, k be a positive integer, and A be the multiplicative subgroup of nonzero k-th powers in Z_p. The goal of this paper is to determine, for a given positive integer s, a value t_s such that if |A| ≫ t_s then every element of Z_p is a sum of s k-th powers. We obtain t_4 = p^{\frac{22}{39} + \in}, t_5 = p^{\frac{15}{29} + \in} and for s s ≥ 6, t_s = p^{\frac{9s+45}{29s+33} + \in}. For s ≥ 24 further improvements are made, such as t_32 = p^{\frac{5}{16} + \in} and t_128 = p^{\frac{1}{4}}. en_US
dc.language.iso en_US en_US
dc.relation.uri http://journals.impan.gov.pl/cgi-bin/aa/pdf?aa163-4-02 en_US
dc.subject Warings problem en_US
dc.subject Exponential sums en_US
dc.subject Sum-Product sets en_US
dc.title Waring's number for large subgroups of double-struck Z_p en_US
dc.type Article (author version) en_US
dc.date.published 2014 en_US
dc.citation.doi 10.4064/aa163-4-2 en_US
dc.citation.epage 325 en_US
dc.citation.issue 4 en_US
dc.citation.jtitle Acta Arithmetica en_US
dc.citation.spage 309 en_US
dc.citation.volume 163 en_US
dc.contributor.authoreid cochrane en_US
dc.contributor.authoreid cpinner en_US
dc.contributor.authoreid cvs en_US

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