Generalized sarwate bounds on the periodic correlation of complex roots of unity sequences

2004 ◽  
Author(s):  
Daiyuan Peng ◽  
Pingzhi Fan
Keyword(s):  
Roots Of Unity ◽  
Complex Roots ◽  
Periodic Correlation

scholarly journals Roots of Elliptic Scator Numbers

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 321
Author(s):  
Manuel Fernandez-Guasti
Keyword(s):  
Abelian Group ◽  
Geometric Interpretation ◽  
Roots Of Unity ◽  
Complex Roots ◽  
De Moivre’S Formula

The Victoria equation, a generalization of De Moivre’s formula in 1+n dimensional scator algebra, is inverted to obtain the roots of a scator. For the qth root in S1+n of a real or a scator number, there are qn possible roots. For n=1, the usual q complex roots are obtained with their concomitant cyclotomic geometric interpretation. For n≥2, in addition to the previous roots, new families arise. These roots are grouped according to two criteria: sets satisfying Abelian group properties under multiplication and sets catalogued according to director conjugation. The geometric interpretation is illustrated with the roots of unity in S1+2.

scholarly journals Generators and Relations for Cyclotomic Units

1966 ◽  
Vol 27 (2) ◽  
pp. 401-407 ◽  
Author(s):  
Hyman Bass
Keyword(s):  
Number Theory ◽  
Roots Of Unity ◽  
Generators And Relations ◽  
Complex Roots ◽  
Complete Set ◽  
Cyclotomic Units

We prove here an unpublished conjecture of Milnor which gives a complete set of multiplicative relations between the numbers e′(ζ) = 1−ζ,where ranges over complex roots of unity. Information of this type is useful in certain areas of topology as well as in number theory.

A note on B- and Br- incomplete topological Abelian groups

1969 ◽  
Vol 66 (2) ◽  
pp. 275-279 ◽  
Author(s):  
L. J. sulley
Keyword(s):  
Abelian Groups ◽  
Roots Of Unity ◽  
Complex Roots

From results of Baker (2) it appeared to be unlikely that, in Hausdorff topological Abelian groups, completeness would be implied by Br- or B-completeness (for definitions, see below). We show here (Corollary 1) that the group of all complex roots of unity, though not complete, is B-complete. Another example, for the suggestion of which we are indebted to Dr J. W. Baker, is used to show (Corollary 2) that B-completeness is not a consequence of Br-completeness. It is proved, however, that B- and Br-complete Hausdorff topological Abelian groups are embedded in their completions in special ways in relation to the closed subgroups of the completions. Also, the completions of B- and Br-complete Hausdorff topological Abelian groups are shown to be, respectively, B- and Br-complete.

scholarly journals Odd Ramanujan Sums of Complex Roots of Unity

2007 ◽  
Vol 14 (1) ◽  
pp. 20-23 ◽  
Author(s):  
Soo-Chang Pei ◽  
Kuo-Wei Chang
Keyword(s):  
Roots Of Unity ◽  
Complex Roots ◽  
Ramanujan Sums
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