Results 191 to 200 of about 165,979,158 (232)

Sum of Divisors in a Ring of Gaussian Integers

Ukrainian Mathematical Journal, 2001
Summary: We construct an asymptotic formula for a summation function for \(\sigma_a(\alpha)\), where \(\sigma_a(\alpha)\) is the sum of the \(a\)-th powers of the norms of divisors of the Gaussian integer \(\alpha\) on an arithmetic progression \(\alpha\sim\alpha_0\pmod\gamma\) and in a narrow sector \(\phi_1\leq\operatorname {arg ...
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Representations of Cyclic Groups in Rings of Integers, I

The Annals of Mathematics, 1962
Let Gk be a cyclic group of order k, and let ZGk denote its group ring over the ring Z of rational integers. We denote by n(ZGk) the number of non-isomorphic indecomposable left ZGk-modules having finite Z-bases. In 1938 Diederichsen [2] proved that n(ZG,) is finite for p a rational prime, and gave an incorrect proof that n(ZG4) is infinite.
Heller, A., Reiner, Irving
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Multiplication Of Polynomials Over The Ring Of Integers

25th Annual Symposium onFoundations of Computer Science, 1984., 2005
Let R be a ring, and let f(/spl alpha/), g(/spl alph/) /spl epsi/ R[/spl alpha/] be univariate polynomials over R of degree n. We Present an algorithm for computing the coefficients of the product f(/spl alpha/)G (/spl alpha/) by O (nlgn) multiplications. This algorithm is based on an algorithm for multiplying polynomials over the ring of integers, and
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Rings: Applications of the integers

1976
In this chapter we assemble some results on rings which we obtain by using a specific knowledge of the natural numbers and the integers. We begin the chapter with some work refining our knowledge of finite and infinite sets. We then routinely study some theorems extending the associative, commutative, and distributive laws to any finite number of ...
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A CONSTRUCTION OF THE RING OF INTEGERS

JP Journal of Algebra, Number Theory and Applications, 2020
Cherniavsky, Yonah, Jarden, Adi
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Residue computations in rings of algebraic integers

International Conference on Acoustics, Speech, and Signal Processing, 2002
Recent work has focused on doing residue computations that use quantization within a particular dense ring of integers in the complex plane. That work is generalized, and it is shown that a class of cubic integers provides a more efficient and less costly solution than other rings of integers which have been considered previously.
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Similarity of matrices with integer spectrum over the ring of integers

Russian Mathematics, 2011
For matrices with integer elements which have the same integer spectrum and whose Jordan form contains no blocks of the same order for one and the same eigenvalue, we propose a quasipolynomial-time algorithm for recognizing their similarity over the ring of integers.
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On successive minima of rings of algebraic integers

1998
We give an account of some largely experimental results about the successive minima of the ring of integers of an algebraic number field endowed with its canonical Euclidean norm. This throws light on some interesting facts which could be important for the algorithmic theory of number fields.
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Rings:Natural numbers and integers

1976
The positive whole numbers are undoubtedly the oldest and most primitive objects of all mathematics. They formed, and still form, the basis from which all other mathematics sprang. Zero appeared upon the mathematical scene later. The natural numbers are so much the genesis of all mathematics that the 19th century mathematician Leopold Kronecker was led
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On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n

Mathematics, 2021
Shariefuddin Pirzada, Yilun Shang, Bilal Ahmad Rather   +2 more
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