Results 11 to 20 of about 170 (40)

On quotients of Riemann zeta values at odd and even integer arguments

, 2013
We show for even positive integers $n$ that the quotient of the Riemann zeta values $\zeta(n+1)$ and $\zeta(n)$ satisfies the equation $$\frac{\zeta(n+1)}{\zeta(n)} = (1-\frac{1}{n}) (1-\frac{1}{2^{n+1}-1}) \frac{\mathcal{L}^\star(\mathfrak{p}_n ...
Kellner, Bernd C.
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Classification and irreducibility of a class of integer polynomials

Open Mathematics
We find all integer polynomials of degree dd that take the values ±1\pm 1 at exactly dd integer arguments, and determine the irreducibility of these polynomials by means of an elementary approach.
Chen Yizhi, Zhao Xiangui, Zhou Xuan
doaj   +1 more source

Squarefree values of polynomial discriminants II

Forum of Mathematics, Pi
We determine the density of integral binary forms of given degree that have squarefree discriminant, proving for the first time that the lower density is positive. Furthermore, we determine the density of integral binary forms that cut out maximal orders
Manjul Bhargava, Arul Shankar, Xiaoheng Wang   +2 more
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Improvements on dimension growth results and effective Hilbert’s irreducibility theorem

Forum of Mathematics, Sigma
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree d, over any global field.
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel, Kien Huu Nguyen, Floris Vermeulen   +4 more
doaj   +1 more source

Higher Mahler measures and zeta functions

, 2009
We consider a generalization of the Mahler measure of a multivariable polynomial $P$ as the integral of $\log^k|P|$ in the unit torus, as opposed to the classical definition with the integral of $\log|P|$. A zeta Mahler measure, involving the integral of
Kurokawa, Nobushige, Lalin, Matilde, Ochiai, Hiroyuki   +2 more
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Reciprocal Monogenic Septinomials of Degree 2n3

Annales Mathematicae Silesianae
We prove a new irreducibility criterion for certain septinomials in ℤ[x], and we use this result to construct infinite families of reciprocal septinomials of degree 2n3 that are monogenic for all n ≥ 1.
Jones Lenny
doaj   +1 more source

On the reducibility type of trinomials

, 2011
Say a trinomial $x^n+A x^m+B \in \Q[x]$ has reducibility type $(n_1,n_2,...,n_k)$ if there exists a factorization of the trinomial into irreducible polynomials in $\Q[x]$ of degrees $n_1$, $n_2$,...,$n_k$, ordered so that $n_1 \leq n_2 \leq ... \leq n_k$.
Bremner, Andrew, Ulas, Maciej
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Counting Perron Numbers by Absolute Value [PDF]

, 2015
We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers.
Calegari, Frank, Huang, Zili
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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
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Class Number Two for Real Quadratic Fields of Richaud-Degert Type [PDF]

, 2009
2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial
Mollin, R. A.
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