Sidon sets with extremal Sidon constants
Colin C. Graham and L. Thomas Ramsey
Proc. Amer. Math. Soc. 83 (1981), 522-526
Primary 43A46; Secondary 20F99
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Abstract: A finitely supported measure on an l.c.a. group is said to be extremal if . If is an extremal measure and is the support of , it follows that the Sidon constant of is , in which case is also said to be extremal. Our results are these. (1) An "independent" union of cosets of a finite subgroup of is extremal if and only if (essentially) divides . (2) Not all extremal subsets of abelian groups have the form described in (1). (3) For any group (abelian or not), the Sidon constant of that group is at least .
I. Cartwright, Robert
B. Howlett, and John
R. McMullen, Extreme values for the Sidon
constant, Proc. Amer. Math. Soc.
81 (1981), no. 4,
601723 (82c:43005), http://dx.doi.org/10.1090/S0002-9939-1981-0601723-X
C. Graham and O.
Carruth McGehee, Essays in commutative harmonic analysis,
Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of
Mathematical Science], vol. 238, Springer-Verlag, New York, 1979. MR 550606
- D. I. Cartwright, R. B. Howlett and J. R. McMullen, Extreme values for the Sidon constant, Proc. Amer. Math. Soc. 81 (1981), 531-537. MR 601723 (82c:43005)
- C. C. Graham and O. C. McGehee, Essays in commutative harmonic analysis, Springer-Verlag, Berlin and New York, 1979. MR 550606 (81d:43001)
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