Results 11 to 20 of about 1,299,040 (282)
Prime Spectrum of the Ring of Adeles of a Number Field
Mathematics, 2022 Much is known about the adele ring of an algebraic number field from the perspective of harmonic analysis and class field theory. However, its ring-theoretical aspects are often ignored.
Álvaro Serrano Holgado
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The tree of primes in a field [PDF]
Cubo, 2010 The product formula of algebraic number theory connects finite and infinite primes in a stringent way, a fact, while not hard to be checked, that has never ceased to be tantalizing.
Wolfgang Rump
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The Number Field Sieve in the Medium Prime Case [PDF]
Lecture Notes in Computer Science, 2006 In this paper, we study several variations of the number field sieve to compute discrete logarithms in finite fields of the form ${\mathbb F}_{p^n}$, with p a medium to large prime. We show that when n is not too large, this yields a $L_{p^n}(1/3)$ algorithm with efficiency similar to that of the regular number field sieve over prime fields.
Antoine Joux, Frederik Vercauteren
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ریاضی و جامعه, 2022 Translator's abstractThis paper deals with one of the important and interesting topics in Number Theory under the title of prime number races, which is less discussed in Persian texts. All prime numbers (except 2) can be written in the form 4n+1 or 4n+3.
Mohammad Reza Esfandiari
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Sensors, 2022 The advent of the Internet of Things (IoT) has enabled millions of potential new uses for consumers and businesses. However, with these new uses emerge some of the more pronounced risks in the connected object domain. Finite fields play a crucial role in
Anissa Sghaier +5 more
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A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes
IEEE Access, 2021 In this article, we study the cycle structure of (3, 19)-regular Tanner’s quasi-cyclic (QC) LDPC codes with code length $19p$ , where $p$ is a prime and $p\equiv 1~(\bmod ~57)$ , and transform the conditions for the existence of cycles of ...
Manjie Zhou +4 more
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Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$ [PDF]
Mathematica Bohemica, 2021 If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational
Julio Pérez-Hernández +1 more
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Computation of Trusted Short Weierstrass Elliptic Curves for Cryptography
Cybernetics and Information Technologies, 2021 Short Weierstrass elliptic curves with underlying hard Elliptic Curve Discrete Logarithm Problem (ECDLP) are widely used in cryptographic applications. A notion of security called Elliptic Curve Cryptography (ECC) security is also suggested in literature
Abhishek Kunal +1 more
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Infinite primes of fields and completions [PDF]
Pacific Journal of Mathematics, 1973 The notion of infinite prime in a ring with identity, defined in the first author's memoir "Finite and infinite primes for rings and fields" (A.M.S Memoir #68), is studied in fields. Extending results of R. Baer and D. W. Dubois, each infinite prime P of a field F is shown to determine a complex place φP of F such that φP{P) is the set of nonnegative ...
Harrison, D. K., Warner, Hoyt D.
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Type-II QC-LDPC Codes From Multiplicative Subgroup of Prime Field
IEEE Access, 2020 A quasi-cyclic (QC) low-density parity-check (LDPC) code is called type-II, if the maximum weight over all circulants appearing in the parity-check matrix has the value of two. On the basis of multiplicative subgroup analysis for the prime field, a novel
Guohua Zhang +4 more
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