TY - JOUR
T1 - An Addition Theorem and Its Arithmetical Application
AU - Freiman, Gregory
AU - Geroldinger, Alfred
PY - 2000/11
Y1 - 2000/11
N2 - We study almost arithmetical multiprogressions, which are defined as certain unions of arithmetical progressions. We prove an addition theorem stating that arbitrary sumsets of such sets are of the same type again. Almost arithmetical multiprogressions appear as sets of lengths in rings of algebraic integers, and the addition theorem will be applied to an arithmetical situation again.
AB - We study almost arithmetical multiprogressions, which are defined as certain unions of arithmetical progressions. We prove an addition theorem stating that arbitrary sumsets of such sets are of the same type again. Almost arithmetical multiprogressions appear as sets of lengths in rings of algebraic integers, and the addition theorem will be applied to an arithmetical situation again.
KW - Addition theorems; sets of lengths
UR - http://www.scopus.com/inward/record.url?scp=0034311209&partnerID=8YFLogxK
U2 - 10.1006/jnth.2000.2521
DO - 10.1006/jnth.2000.2521
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AN - SCOPUS:0034311209
SN - 0022-314X
VL - 85
SP - 59
EP - 73
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 1
ER -