We present a construction of expander graphs obtained from Cayley graphs of narrow ray class groups, whose eigenvalue bounds follow from the Generalized Riemann Hypothesis. Our result implies that the Cayley graph of (Z/qZ)∗ with respect to small prime generators is an expander. As another application, we show that the graph of small prime degree isogenies between ordinary elliptic curves achie...

In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem Ax = λBx are needed. If exact linear solves with A − σB are available, implicitly restarted Arnoldi with purification is a common approach for problems where B is positive semidefinite. In this paper, a new approach based on implicitly restarted Arnoldi will be presented that avoids most of ...

A new class of structured polynomial eigenproblems arising in the stability analysis of time-delay systems is identified and analyzed together with new types of closely related structured polynomials. Relationships between these polynomials are established via the Cayley transformation. Their spectral symmetries are revealed, and structure-preserving linearizations constructed. A structured Sch...

In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem Ax = λBx are needed. If exact linear solves with A−σB are available, implicitly restarted Arnoldi with purification is a common approach for problems where B is positive semidefinite. In this paper, a new approach based on implicitly restarted Arnoldi will be presented that avoids most of th...

Assuming the well known conjecture that for any γ > 0 and x sufficiently large the interval [x, x+xγ ] always contains a prime number, we prove the following unexpected result: There exist numbers 0 < ρ < 1 arbitrarily close to 0, and arbitrarily large primes q, such that if S is any subset of Z/qZ of density at least ρ, having the least number of 3-term arithmetic progressions among all such s...

Este artículo pertenece al proyecto: “Estudio del magmatismo Mesozoico y sus implicancias en la determinación de un modelo exploración geológico-estructural relacionado con ocurrencia Yacimientos tipo IOCG Cordillera costa llanuras pre-andinas los Andes Peruanos” elaborado dentro convenio INGEMMET UNMSM. Durante las actividades campo se enfatizó cartografía geológica zonas C-1 C-2, identificand...

Given an integer q and a polynomial f∈Zq[X] of degree d with coefficients in the residue ring Zq=Z/qZ, we obtain new results concerning number solutions to congruences form y≡f(x)(modq), variables lying some cube B side length H. Our argument uses ideas Cilleruelo, Garaev, Ostafe Shparlinski which reduces problem Vinogradov mean value theorem lattice point counting problem. We treat differently...

Let ${\mathcal A}$ be a generalized $q$-Weyl algebra, it is generated by $u$, $v$, $Z$, $Z^{-1}$ with relations $ZuZ^{-1}=q^2u$, $ZvZ^{-1}=q^{-2}v$, $uv=P\big(q^{-1}Z\big)$, $vu=P(qZ)$, where $P$ Laurent polynomial. A Hermitian form $(\cdot,\cdot)$ on called invariant if $(Za,b)=\big(a,bZ^{-1}\big)$, $(ua,b)=(a,sbv)$, $(va,b)=\big(a,s^{-1}bu\big)$ for some $s\in {\mathbb C}$ $|s|=1$ and all $a,...

Given an integer q ≥ 2 and a number θ ∈ (0, 1], consider the collection of all subsets of Zq := Z/qZ having at least θq elements. Among the sets in this collection, suppose S is any one having the minimal number of three-term arithmetic progressions, where in our terminology a three-term arithmetic progression is a triple (x, y, z) ∈ S3 satisfying x + y ≡ 2z (mod q). Note that this includes tri...