Geodesic
Fuglede's conjecture on cyclic groups of order $p^n q$
Discrete analysis (2017) Cet article a éte moissonné depuis la source Scholastica

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We show that the spectral set conjecture by Fuglede holds in the setting of cyclic groups of order $p^n q$, where $p$, $q$ are distinct primes and $n\geq1$. This means that a subset $E$ of such a group $G$ tiles the group by translation ($G$ can be partitioned into translates of $E$) if and only if there exists an orthogonal basis of $L^2(E)$ consisting of group characters. The main ingredient of the present proof is the structure of vanishing sums of roots of unity of order $N$, where $N$ has at most two prime divisors; the extension of this proof to the case of cyclic groups of order $p^n q^m$ seems therefore feasible. The only previously known infinite family of cyclic groups, for which Fuglede's conjecture is verified in both directions, is that of cyclic $p$-groups, i.e. $\mathbb{Z}_{p^n}$.
Publié le : 
@article{DAS_2017_a8,
     author = {Romanos-Diogenes Malikiosis and Mihail N. Kolountzakis},
     title = {Fuglede's conjecture on cyclic groups of order $p^n q$},
     journal = {Discrete analysis},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2017_a8/}
}
TY  - JOUR
AU  - Romanos-Diogenes Malikiosis
AU  - Mihail N. Kolountzakis
TI  - Fuglede's conjecture on cyclic groups of order $p^n q$
JO  - Discrete analysis
PY  - 2017
UR  - http://geodesic.mathdoc.fr/item/DAS_2017_a8/
LA  - en
ID  - DAS_2017_a8
ER  - 
%0 Journal Article
%A Romanos-Diogenes Malikiosis
%A Mihail N. Kolountzakis
%T Fuglede's conjecture on cyclic groups of order $p^n q$
%J Discrete analysis
%D 2017
%U http://geodesic.mathdoc.fr/item/DAS_2017_a8/
%G en
%F DAS_2017_a8
Romanos-Diogenes Malikiosis; Mihail N. Kolountzakis. Fuglede's conjecture on cyclic groups of order $p^n q$. Discrete analysis (2017). http://geodesic.mathdoc.fr/item/DAS_2017_a8/