Generalized Bounds on Partial Aperiodic Correlation of Complex Roots of Unity Sequences

2006 ◽  
pp. 342-350
Author(s):  
Lifang Feng ◽  
Pingzhi Fan
Keyword(s):  
Roots Of Unity ◽  
Complex Roots

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We prove here an unpublished conjecture of Milnor which gives a complete set of multiplicative relations between the numbers e′(ζ) = 1−ζ,where ranges over complex roots of unity.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.

scholarly journals Optimization of Resource Utilization of Fast Fourier Transform

2018 ◽  
Vol 6 (3) ◽  
pp. 186
Author(s):  
Subhash Chandra Yadav ◽  
Pradeep Juneja ◽  
R. G. Varshney
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Resource Utilization ◽  
Roots Of Unity ◽  
Font Size ◽  
Complex Roots ◽  
Fft Algorithms

<span style="font-size: 9pt; font-family: 'Times New Roman', serif;" lang="EN-IN">This paper considers the optimization of resource utilization for three FFT algorithms, as it pertains not to the input samples or output modes, but to the <em>twiddle factors </em>that arise in Cooley-Tukey FFT algorithms. Twiddle factors are a set of complex roots of unity, fixed by the transform order for the particular algorithm. This paper shows the comparison between three known FFT algorithms, DIT-FFT, DIF-FFT and G<sup>T</sup> algorithm. All these algorithms are implemented on FPGA (Spartan-3 XC3S4000l-4fg900) with XILINX 10.1 ISE.</span>

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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