Results 71 to 80 of about 1,203,239 (192)
On some finiteness results for unramified cohomology [PDF]
arXiv, 2016 We obtain several finiteness results for the unramified cohomology of function fields of algebraic varieties defined over fields of type (F'_m), a class that includes algebraically closed fields, finite fields, local fields, and some higher local fields of characteristic 0.
arxiv
On the Lehmer's totient problem on Number Fields [PDF]
arXiv, 2020 Lehmer's totient problem asks if there exists a composite number $d$ such that its totient divide $d-1$. In this article we generalize the Lehmer's totient problem in algebraic number fields. We introduce the notion of a Lehmer number. Lehmer numbers are defined to be the natural numbers which obey the Lehmer's problem in the ring of algebraic integers
arxiv
On the quantum security of high-dimensional RSA protocol
Journal of Mathematical CryptologyThe idea of extending the classical RSA protocol using algebraic number fields was introduced by Takagi and Naito (Construction of RSA cryptosystem over the algebraic field using ideal theory and investigation of its security.
Rahmani Nour-eddine +3 more
doaj +1 more source
Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials [PDF]
arXiv, 2009 In this paper we prove that assuming Schanuel's conjecture, an exponential polynomial in one variable over the algebraic numbers has only finitely many algebraic solutions. This implies a positive answer to Shapiro's conjecture for exponential polynomials over the algebraic numbers for pseudoexponential fields as well as for any algebraically closed ...
arxiv
On the number of points over finite fields on varieties related to cluster algebras [PDF]
arXiv, 2009 We compute the number of points over finite fields of some algebraic varieties related to cluster algebras of finite type. More precisely, these varieties are the fibers of the projection map from the cluster variety to the affine space of coefficients.
arxiv
Quantum Algorithm for Computing the Period Lattice of an Infrastructure [PDF]
, 2012 We present a quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions.
Fontein, Felix, Wocjan, Pawel
core
Orders of Quaternion Algebras with Involution [PDF]
arXiv, 2016 We introduce the notion of maximal orders over quaternion algebras with orthogonal involution and give a classification over local fields, and a partial classification over algebraic number fields.
arxiv
On finite arithmetic groups [PDF]
International Journal of Group Theory, 2013 Let $F$ be a finite extension of $Bbb Q$, ${Bbb Q}_p$ or a globalfield of positive characteristic, and let $E/F$ be a Galois extension.We study the realization fields offinite subgroups $G$ of $GL_n(E)$ stable under the naturaloperation of the Galois ...
Dmitry Malinin
doaj
On the Genus number of Algebraic groups [PDF]
arXiv, 2013 We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action of these groups on their Lie algebras. We also prove that the genus number of a connected reductive algebraic group
arxiv
Notes on the Theory of Algebraic Numbers [PDF]
arXiv, 2015 A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on the texts of E. Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag, 1981 (English translation by G.
arxiv