Positive definiteness in additive number theory (CROSBI ID 552653)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | domaća recenzija
Podaci o odgovornosti
Ninčević, Marina ; Slijepčević, Siniša
engleski
Positive definiteness in additive number theory
The additive number theory questions related to e.g. existing of arithmetic sequences in subsets of integers, relied on application of Fourier analysis and the Hardy – Littlewood method. We develop a set of alternative tools related to positive definiteness of complex functions on rings Z_n. We also introduce the notion of strong positive definiteness, and develop characterizations of it. It is then shown that understanding strong positive definiteness of general complex functions on Z_n is equivalent to solving various problems in the additive number theory. We conclude with an application to estimates related to the Sarkozy theorem on square differences in subsets of integers.
Positive definiteness; Van der Corput property; Poincare property; perfect squares
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Podaci o prilogu
2008.
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objavljeno
Podaci o matičnoj publikaciji
4. hrvatski matematički kongres : knjiga sažetaka
Podaci o skupu
Hrvatski matematički kongres (4 ; 2008)
predavanje
17.07.2008-20.07.2008
Osijek, Hrvatska