Results 31 to 40 of about 59,442 (147)

Integral closure of rings of integer-valued polynomials on algebras

, 2014
Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e.
G. Peruginelli, G. Peruginelli, J.-P. Cahen, J.P. Serre, K.A. Loper, L.E. Dickson, N. Bourbaki, R. Gilmer, S. Evrard, S. Frisch, T.Y. Lam   +10 more
core   +1 more source

Primary decomposition of the ideal of polynomials whose fixed divisor is divisible by a prime power [PDF]

, 2010
We characterize the fixed divisor of a polynomial $f(X)$ in $\mathbb{Z}[X]$ by looking at the contraction of the powers of the maximal ideals of the overring ${\rm Int}(\mathbb{Z})$ containing $f(X)$. Given a prime $p$ and a positive integer $n$, we also
Giulio Peruginelli, Anderson, Bandini, Chabert, Cahen, Cahen, Chapman, Dickson, Gunji, Keller, Lewis, Loper, McQuillan, Niven, Northcott   +14 more
core   +2 more sources

Relative polynomial closure and monadically Krull monoids of integer-valued polynomials [PDF]

, 2015
Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f in Int(D), we explicitly construct a divisor homomorphism from [f], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N_0 ...
Frisch, Sophie
core  

Strong asymptotics for Jacobi polynomials with varying nonstandard parameters [PDF]

, 2004
Strong asymptotics on the whole complex plane of a sequence of monic Jacobi polynomials $P_n^{(\alpha_n, \beta_n)}$ is studied, assuming that $$ \lim_{n\to\infty} \frac{\alpha_n}{n}=A, \qquad \lim_{n\to\infty} \frac{\beta _n}{n}=B, $$ with $A$ and $B ...
A. A. Gonchar, A. B. J. Kuijlaars, A. B. J. Kuijlaars, A. B. J. Kuijlaars, A. B. J. Kuijlaars, A. Fokas, A. I. Aptekarev, A. Martínez-Finkelshtein, A. Martínez-Finkelshtein, C. Bosbach, C. Pommerenke, D. S. Moak, E. B. Saff, F. W. J. Olver, G. Szegö, H. Dette, H. Stahl, J. Baik, K. Driver, K. Driver, K. Driver, K. Strebel, L.-C. Chen, M. Abramowitz, N. M. Temme, P. A. Deift, P. Deift, P. Deift, P. Deift, P. Duren, P. Duren, S. Kamvissis, W. Gawronski   +32 more
core   +4 more sources

Interpolation by Integer-Valued Polynomials

Journal of Algebra, 1999
The author pursues two directions to construct interpolating integer-valued polynomials on Krull domains \(R\), that means, given distinct \(a_1, \dots, a_n\in S\leq R\) and \(b_1, \dots, b_n\in R\) there exists an \(f\in \text{Int}(S,R)= \{f\in K[x] \mid f(S)\subseteq R\}\), \(K\) being the quotient field of \(R\), with \(f(a_i) =b_i\), \(i=1, \dots,n\
openaire   +1 more source

On multivariable cumulant polynomial sequences with applications

, 2016
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method.
Di Nardo, E.
core   +1 more source

Riemann–Roch for the ring $\mathbb{Z}$

Comptes Rendus. Mathématique
We show that by working over the absolute base $\mathbb{S}$ (the categorical version of the sphere spectrum) instead of ${\mathbb{S}[\pm 1]}$ improves our previous Riemann–Roch formula for ${\overline{\operatorname{Spec}\mathbb{Z}}}$. The formula equates
Connes, Alain, Consani, Caterina
doaj   +1 more source

Values of random polynomials at integer points

Journal of Modern Dynamics, 2018
to appear, Journal of Modern ...
Athreya, Jayadev S., Margulis, Gregory
openaire   +2 more sources

Split Primes and Integer-Valued Polynomials

Journal of Number Theory, 1993
Let \(R\) be a Dedekind domain with finite residue fields, \(K\) its field of fractions, and denote by \(I\) the ring of integer-valued polynomials over \(R\), \(I=\{g(x)\in K[x];\;g(R)\subseteq R\}\). Let \(L\) be a finite separable extension of \(K\) and \(S\) be the integral closure of \(R\) in \(L\). For a nonzero prime ideal \(P\) of \(S\) write \(
openaire   +2 more sources

Integer-valued polynomials, Prüfer domains, and localization [PDF]

Proceedings of the American Mathematical Society, 1993
Let A A be an integral domain with quotient field K K and let Int ⁡ ( A ) \operatorname {Int} (A) be the ring of integer-valued polynomials on A : { P ∈ K [ X ] | P (
openaire   +2 more sources