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A Pollard Type Result for Restricted Sums

✍ Scribed by Cristina Caldeira; J.A Dias da Silva

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
324 KB
Volume
72
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let F be an arbitrary field. Let p be the characteristic of F in case of finite characteristic and if F has characteristic 0. Let A be a finite subset of F.

c be one-half of the cardinality of the set of pairs (a, b) satisfying a{b and a+b=c. Denote by + (R) i the cardinality of the set [c # Ã 2 A | & (R) c i]. We prove that, for t=1, ..., w |A|Â2x , t i=1 + (R) i t min[ p, 2(|A| &t)&1]. For F=Z p and t=1 we get the Erdo s Heilbronn conjecture, first proved by

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