Results 281 to 290 of about 32,005 (324)
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A Development of Associative Algebra and an Algebraic Theory of Numbers, I
Mathematics Magazine, 1952in which if we denote a particular element by Ck, its immediate successor in this is CkJ, where k denotes a natural number and k' its immediate successor in the set of natural numbers. We then introduced in addition to these symbols the symbol + (called a plus sign); x (called a multiplication sign); and (, called a left parenthesis symbol; and ...
M. W. Weaver, H. S. Vandiver
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1991
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as ...
Martin J. Taylor, A. Fröhlich
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This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as ...
Martin J. Taylor, A. Fröhlich
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On a problem in algebraic number theory
Mathematical Proceedings of the Cambridge Philosophical Society, 1996Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq
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Instantons and the large N=4 algebra
Journal of Physics A: Mathematical and TheoreticalWe investigate the differential geometry of the moduli space of instantons on S3×S1. Extending previous results, we show that a sigma-model with this target space can be expected to possess a large N=4 superconformal symmetry, supporting speculations ...
Edward Witten
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Foundations of the Theory of Algebraic Numbers
Nature, 1932THIS is the first volume of Prof. Hancock's work and is intended as an introduction to the second volume. Its size shows that he is engaged in no light task. His object is to help in making the theory of algebraic numbers more accessible, more attractive, and less difficult.
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Computer Algebra in the Service of Mathematical Physics and Number Theory
Computers in Mathematics, 2020D. Chudnovsky, G. Chudnovsky
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Algebraic Theory of Complex Numbers
1962Before defining complex numbers let us briefly review the more familiar types of numbers and let us examine why there are different kinds of numbers.
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Algebraic Aspects of Number Theory
2014Chapter 10 discusses some more interesting properties of integers, in particular, properties of prime numbers and primality testing by using the tools of modern algebra, which are not studied in Chap. 1. In addition, the applications of number theory, particularly those directed towards theoretical computer science, are presented.
Mahima Ranjan Adhikari, Avishek Adhikari
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JP Journal of Algebra Number Theory and Applications, 2018
D. Gómez-Ramírez +4 more
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D. Gómez-Ramírez +4 more
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Algebraic Number Theory: Cyclotomy
2018In this chapter, we return to one of Gauss’s favourite themes, cyclotomic integers, and look at how they were used by Kummer, one of the leaders of the next generation of German number theorists. French and German mathematicians did not keep up-to-date with each other’s work, and for a brief, exciting moment in Paris in 1847 it looked as if the ...
Jeremy Gray, Jeremy Gray
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