Results 61 to 70 of about 631,644 (215)
Distribution of primes represented by polynomials and Multiple Dedekind zeta functions [PDF]
arXiv, 2022 n this paper, we state several conjectures regarding distribution of primes and of pairs of primes represented by irreducible homogeneous polynomial in two variables $f(a,b)$. We formulate conjectures with respect to the slope $t=b/a$ for any irreducible polynomial $f$. Here, we formulate a conjecture for all irreducible polynomials. We also consider
arxiv
Infinite Towers of Galois Defect Extensions of Kaplansky Fields
Annales Mathematicae Silesianae, 2018 We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of ...
Blaszczok Anna
doaj +1 more source
Explicit Bound for the Prime Ideal Theorem in Residue Classes [PDF]
arXiv, 2017 We give explicit numerical estimates for the generalized Chebyshev functions. Explicit results of this kind are useful for estimating of computational complexity of algorithms which generates special primes. Such primes are needed to construct an elliptic curve over prime field using complex multiplication method.
arxiv
Nature Communications, 2023 The polymorphic transition from 2H to 1 $${T}^{{\prime} }$$ T ′ -MoTe2, which was thought to be induced by high-energy photon irradiation among many other means, has been intensely studied for its technological relevance in nanoscale transistors due to ...
Jiaojian Shi +15 more
doaj +1 more source
A note on expansion in prime fields
, 2018 Let $ , \in (0,1]$, and $k \geq \exp(122 \max\{1/ ,1/ \})$. We prove that if $A,B$ are subsets of a prime field $\mathbb{Z}_{p}$, and $|B| \geq p^ $, then there exists a sum of the form $$S = a_{1}B \pm \ldots \pm a_{k}B, \qquad a_{1},\ldots,a_{k} \in A,$$ with $|S| \geq 2^{-12}p^{- }\min\{|A||B|,p\}$.
Orponen, Tuomas, Venieri, Laura
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Properties of Primes and Multiplicative Group of a Field [PDF]
Formalized Mathematics, 2009 In the [16] has been proven that the multiplicative group Z/pZ∗ is a cyclic group. Likewise, finite subgroup of the multiplicative group of a field is a cyclic group. However, finite subgroup of the multiplicative group of a field being a cyclic group has not yet been proven.
Arai, Kenichi, Okazaki, Hiroyuki
openaire +3 more sources
Number-theoretic expressions obtained through analogy between prime factorization and optical interferometry [PDF]
, 2011 Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in order to obtain, for the first time, analytic expressions for closely related functions, including the number of ...
arxiv +1 more source
Explicit Factorization of Prime Integers in Quartic Number Fields defined by $X^4+aX+b$ [PDF]
arXiv, 2010 For every prime integer $p$, an explicit factorization of the principal ideal $p\z_K$ into prime ideals of $\z_K$ is given, where $K$ is a quartic number field defined by an irreducible polynomial $X^4+aX+b\in\z[X]$.
arxiv
The smallest inert prime in a cyclic number field of prime degree [PDF]
Mathematical Research Letters, 2013 Fix an odd prime `. For each cyclic extension K/Q of degree `, let nK denote the least rational prime which is inert in K, and let rK be the least rational prime which splits completely in K. We show that nK possesses a finite mean value, where the average is taken over all such K ordered by conductor.
openaire +1 more source
Sets of Completely Decomposed Primes in Extensions of Number Fields [PDF]
arXiv, 2015 We introduce the notion of saturated sets of primes of an algebraic number field and prove an analogue of Riemann's existence theorem for the decomposition groups of infinite stably saturated sets of primes.
arxiv