Results 51 to 60 of about 545 (160)
The degrees of the cyclotomic extension fields
Linear Algebra and its Applications, 1993 The following question is investigated: ``Suppose \(r\) and \(s\) are relatively prime positive integers and \(\xi_ r\), \(\xi_ s\), \(\xi_{rs}\) primitive roots of unity. When for positive integers \(a\), \(b\) and \(c\) is there a field \(K\) of characteristic zero with \(| K(\xi_{rs}): K|=a\), \(| K(\xi_ r): K| =b\), and \(| K(\xi_ s):K| =c ...
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A P‐adic class formula for Anderson t‐modules
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
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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
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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
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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
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The class number of cyclotomic function fields
, 1981 Let k be a rational function field over a finite field. Carlitz and Hayes have described a family of extensions of k which are analogous to the collection of cyclotomic extensions {Q(ζm)| m ≥ 2} of the rational field Q.
Rosen, Michael, Galovich, Steven
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Endomorphisms of Abelian varieties, cyclotomic extensions and Lie algebras [PDF]
Sbornik: Mathematics, 2011 9 ...
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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
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Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions [PDF]
, 2010 This paper describes an extremely efficient squaring operation in the so-called ‘cyclotomic subgroup’ of $\mathbb{F}_{q^6}^{\times}$, for $q \equiv 1 \bmod{6}$. Our result arises from considering the Weil restriction of scalars of this group from $\mathbb{F}_{q^6}$ to $\mathbb{F}_{q^2}$, and provides efficiency improvements for both pairing-based and ...
Robert Granger, Michael Scott
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