Study of Additive and Multiplicative Relations Connecting Conjugate Algebraic Numbers

K.PRASHANTH; Dr. Vandana Malviya

Study of Additive and Multiplicative Relations Connecting Conjugate Algebraic Numbers

Authors: K.PRASHANTH, Dr. Vandana Malviya

Unique Paper ID: 156142
Volume: 9
Issue: 2
PageNo: 8-11

Keywords: Additive numbers Multiplicative Conjugate Algebraic Numbers

Abstract:
The present work look at what algebraic numbers may be represented with the aid of using a manufactured from algebraic numbers conjugated over a set wide variety area K in constant integer powers. The hassle is nontrivial if the sum of those integer powers is identical to zero. The norm of this sort of wide variety over K ought to be a root of harmony. We display that there are infinitely many algebraic numbers whose norm over K is a root of harmony and which can not be represented with the aid of using this sort of product. Conversely, each algebraic wide variety may be expressed with the aid of using each sufficiently lengthy product in algebraic numbers conjugate over K. We additionally assemble non symmetric algebraic numbers, i.e., algebraic numbers such that no factors of the corresponding Galois organization performing on the entire set in their conjugates shape a Latin square. The dependence family members among answer techniques, algorithms, and parts end up apparent. Fracture algorithms may be obviously forged on this framework. Solutions primarily based totally on manipulate equations also are immediately included as equality constraints. The arbitrary parts may be used so long as the ensuing directed graph is acyclic. It is likewise proven that graph walls and orderings need to be finished withinside the innermost a part of the algorithm, a truth with a few ordinary consequences. In terms of the Legendre image, the law of quadratic reciprocity for notable odd primes states. A reciprocity law is a generalization of the law of quadratic reciprocity. The class huge type of approach relates many critical invariants of a whole lot of problem to a completely unique charge of its Dedekind zeta function.

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Cite This Article

ISSN: 2349-6002
Volume: 9
Issue: 2
PageNo: 8-11

Study of Additive and Multiplicative Relations Connecting Conjugate Algebraic Numbers

Available:https://ijirt.org/Article?manuscript=156142

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