Results 31 to 40 of about 7,243 (134)
Heuristics for anti-cyclotomic $\mathbb{Z}_p$-extensions
, 2022 This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model `how often' the $p$-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent.
Kundu, Debanjana +1 more
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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
The order of the reductions of an algebraic integer
, 2014 Let K be a number field, and let a be a non-zero element of K. Fix some prime number l. We compute the density of the following set: the primes p of K such that the multiplicative order of the reduction of a modulo p is coprime to l (or, more generally ...
Perucca, Antonella
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Lorentz groups of cyclotomic extensions
, 2020 In this (mostly historical) note we show how a unified Kummer-Artin-Schreier sequence from [W], [SOS] may be recovered from the relativistic velocity addition law.
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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
Lower bounds for heights in cyclotomic extensions
Journal of Number Theory, 2010 Let \(f(x) = a_{0} \prod_{i=1}^{d} (x-\alpha_{i}) = a_{0}x^{n}+a_{1}x^{n-1}+ \cdots + a_{n}\) be an irreducible polynomial with integer coefficients. The Mahler measure of \(f\) is defined to be \(M(f) =\prod_{i=1}^{d}\max \{ 1, |\alpha_{i}| \}\). If \(\alpha \neq 0\) is a root of \(f\), then the absolute logarithmic height \(h(\alpha)\) of \(\alpha ...
Ishak, M.I.M. +3 more
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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
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
Akashi series, characteristic elements and congruence of Galois representations
, 2015 In this paper, we compare the Akashi series of the Pontryagin dual of the Selmer groups of two Galois representations over a strongly admissible p-adic Lie extension.
Lim, Meng Fai
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International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.For nonzero coprime integers a and b, a positive integer l is said to be good with respect to a and b if there exists a positive integer k such that l divides ak + bk. Since the early 1990s, the notion of good integers has attracted considerable attention from researchers. This continued interest stems from both their elegant number‐theoretic structure
Somphong Jitman, Anwar Saleh Alwardi
wiley +1 more source