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In this paper, we study dot-product sets and k -simplices in $$\mathbb {Z}_n^d$$ Z n d for odd n , where $$\mathbb {Z}_n$$ Z n is the ring of residues… Click to show full abstract
In this paper, we study dot-product sets and k -simplices in $$\mathbb {Z}_n^d$$ Z n d for odd n , where $$\mathbb {Z}_n$$ Z n is the ring of residues modulo n . We show that if E is sufficiently large then the dot-product set of E covers the whole ring. In higher dimensional cases, if E is sufficiently large then the set of simplices and the set of dot-product simplices determined by E , up to congurence, have positive densities.
Keywords:
dot product;
product;
finite rings;
sets simplices;
product sets;
simplices finite
Journal Title: Journal of Fourier Analysis and Applications
Year Published: 2022
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Journal Title: Journal of Fourier Analysis and Applications
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!