Search results for "number theory"
showing 10 items of 988 documents
"Table 1" of "Measurement of the (anti-)$^{3}$He elliptic flow in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV"
2020
Event-plane resolution $R_{\Psi_{2}}$ of the second harmonic as a function of the collision centrality.
Теорiя чисел: лекцiи проф. Ландау, читанныя в Гётингенском университетѣ
1911
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
An Arakelov inequality in characteristic p and upper bound of p-rank zero locus
2008
In this paper we show an Arakelov inequality for semi-stable families of algebraic curves of genus $g\geq 1$ over characteristic $p$ with nontrivial Kodaira-Spencer maps. We apply this inequality to obtain an upper bound of the number of algebraic curves of $p-$rank zero in a semi-stable family over characteristic $p$ with nontrivial Kodaira-Spencer map in terms of the genus of a general closed fiber, the genus of the base curve and the number of singular fibres. An extension of the above results to smooth families of Abelian varieties over $k$ with $W_2$-lifting assumption is also included.
Non-archimedean hyperbolicity and applications
2018
Inspired by the work of Cherry, we introduce and study a new notion of Brody hyperbolicity for rigid analytic varieties over a non-archimedean field $K$ of characteristic zero. We use this notion of hyperbolicity to show the following algebraic statement: if a projective variety admits a non-constant morphism from an abelian variety, then so does any specialization of it. As an application of this result, we show that the moduli space of abelian varieties is $K$-analytically Brody hyperbolic in equal characteristic zero. These two results are predicted by the Green-Griffiths-Lang conjecture on hyperbolic varieties and its natural analogues for non-archimedean hyperbolicity. Finally, we use …
An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae
2007
Thedecades around 1800were not a period inwhich puremathematics in general, and number theory in particular, flourished in Italy, see [Bottazzini 1994]. It is significant in this respect that Joseph Louis Lagrange, whose birth and early studies took place in Torino, finally became a prominent representative of the Frenchmathematical school and that, decades later, Guglielmo Libri still spent most of his academic career in France. Thus, Gauss’s Disquisitiones Arithmeticae did not have an immediate resonance in Italian mathematical circles. Gianfrancesco Malfatti, a professor in Ferrara, already seventy years old at the time of the publication of theDisquisitiones Arithmeticae, was one of the…
The exact bounds for the degree of commutativity of a p-group of maximal class, II
2004
AbstractLet G be a p-group of maximal class. Since the pioneer work of Blackburn in 1958 (cf. [N. Blackburn, Acta Math. 100 (1958) 45–92]), several authors have obtained information about the degree of commutativity c of G, in order to precise which the defining relations of G are (cf. [N. Blackburn, Acta Math. 100 (1958) 45–92; R. Shepherd, PhD Thesis, University of Chicago, 1970; C.R. Leedham-Green, S. McKay, Quart. J. Math. Oxford Ser. (2) 27 (1976) 297–311, Quart. J. Math. Oxford Ser. (2) 29 (1978) 175–186, 281–299; G.A. Fernández-Alcober, J. Algebra 174 (1995) 523–530; A. Vera-López, J.M. Arregi, F.J. Vera-López, Comm. Algebra 23 (1995) 2765–2795, Math. Proc. Cambridge Philos. Soc. 122…
An improvement of a bound of Green
2012
A p-group G of order pn (p prime, n ≥ 1) satisfies a classic Green's bound log p |M(G)| ≤ ½n(n - 1) on the order of the Schur multiplier M(G) of G. Ellis and Wiegold sharpened this restriction, proving that log p |M(G)| ≤ ½(d - 1)(n + m), where |G′| = pm(m ≥ 1) and d is the minimal number of generators of G. The first author has recently shown that log p |M(G)| ≤ ½(n + m - 2)(n - m - 1) + 1, improving not only Green's bound, but several other inequalities on |M(G)| in literature. Our main results deal with estimations with respect to the bound of Ellis and Wiegold.
Additivity of affine designs
2020
We show that any affine block design $$\mathcal{D}=(\mathcal{P},\mathcal{B})$$ is a subset of a suitable commutative group $${\mathfrak {G}}_\mathcal{D},$$ with the property that a k-subset of $$\mathcal{P}$$ is a block of $$\mathcal{D}$$ if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design $$\mathcal{D}$$ is the group of automorphisms of $${\mathfrak {G}}_\mathcal{D}$$ that leave $$\mathcal P$$ invariant. Whenever k is a prime p, $${\mathfrak {G}}_\mathcal{D}$$ is an elementary abelian p-group.
A coincidence-point problem of Perov type on rectangular cone metric spaces
2017
We consider a coincidence-point problem in the setting of rectangular cone metric spaces. Using alpha-admissible mappings and following Perov's approach, we establish some existence and uniqueness results for two self-mappings. Under a compatibility assumption, we also solve a common fixed-point problem.