Results 41 to 50 of about 12,236 (229)
Ordinary primes for GL2$\operatorname{GL}_2$‐type abelian varieties and weight 2 modular forms
Mathematika, Volume 72, Issue 2, April 2026.Abstract Let A$A$ be a g$g$‐dimensional abelian variety defined over a number field F$F$. It is conjectured that the set of ordinary primes of A$A$ over F$F$ has positive density, and this is known to be true when g=1,2$g=1, 2$, or for certain abelian varieties with extra endomorphisms.
Tian Wang, Pengcheng Zhang
wiley +1 more source
Harbingers of Artin's Reciprocity Law. II. Irreducibility of Cyclotomic Polynomials [PDF]
, 2012 In the first article of this series we have presented the history of auxiliary primes from Legendre's proof of the quadratic reciprocity law up to Artin's reciprocity law.
Lemmermeyer, Franz
core
Small-span Hermitian matrices over quadratic integer rings
, 2013 Building on the classification of all characteristic polynomials of integer symmetric matrices having small span (span less than 4), we obtain a classification of small-span polynomials that are the characteristic polynomial of a Hermitian matrix over ...
Greaves, Gary
core +1 more source
p$p$‐adic equidistribution and an application to S$S$‐units
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We prove a Galois equidistribution result for torsion points in Gmn$\mathbb {G}_m^n$ in the p$p$‐adic setting for test functions of the form log|F|p$\log |F|_p$ where F$F$ is a nonzero polynomial with coefficients in the field of complex p$p$‐adic numbers.
Gerold Schefer
wiley +1 more source
On the non-idealness of cyclotomic families of pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2014 Let k=2mpn$k=2^mp^n$ for an odd prime p and integers m ≥ 0 and n ≥ 0. We obtain lower bounds for the ρ-values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r(x)=Φk(x)$r(x)=\Phi _k(x)$.
Sha Min
doaj +1 more source
Cyclotomy and permutation polynomials of large indices [PDF]
, 2012 We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way.
Wang, Qiang
core
Binary Cyclic Codes from Explicit Polynomials over $\gf(2^m)$
, 2013 Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over finite fields
Ding, Cunsheng, Zhou, Zhengchun
core +2 more sources
Hypergeometric motives from Euler integral representations
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We revisit certain one‐parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of L$L$‐series attached to nondegenerate ...
Tyler L. Kelly, John Voight
wiley +1 more source
A probabilistic approach to value sets of polynomials over finite fields [PDF]
, 2014 In this paper we study the distribution of the size of the value set for a random polynomial with degree at most $q-1$ over a finite field $\mathbb{F}_q$.
Gao, Zhicheng, Wang, Qiang
core
Corrigendum to New Generalized Cyclotomic Binary Sequences of Period $p^2$
, 2017 New generalized cyclotomic binary sequences of period $p^2$ are proposed in this paper, where $p$ is an odd prime. The sequences are almost balanced and their linear complexity is determined.
Helleseth, Tor +3 more
core +1 more source