Results 61 to 70 of about 1,812,540 (189)
Prismatic F‐crystals and Wach modules
Proceedings of the London Mathematical Society, Volume 133, Issue 1, July 2026.Abstract We show that the category of analytic/completed prismatic F-crystals$F\text{-crystals}$ on the absolute prismatic site of a small (unramified at p$p$) base ring is naturally equivalent to the category of relative Wach modules from the theory of (φ,Γ)-modules$(\varphi, \Gamma)\text{-modules}$.
Abhinandan
wiley +1 more source
Physics Letters BWe identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields Q(ζp) (ζp=e2πip) for general prime p≥3. This code-lattice construction is a generalization of
Shun'ya Mizoguchi, Takumi Oikawa
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Motivic mirror symmetry and χ$\chi$‐independence for Higgs bundles in arbitrary characteristic
Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.Abstract We prove that the (twisted orbifold) motives of the moduli spaces of SLn$\mathrm{SL}_n$ and PGLn$\mathrm{PGL}_n$‐Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is invertible are isomorphic in Voevodsky's triangulated category of motives.
Victoria Hoskins, Simon Pepin Lehalleur
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Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros +3 more
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On the Applications of Cyclotomic Fields in Introductory Number Theory [PDF]
, 2013 In this essay, we study and comment on two number theoretical applications on prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime).
Gaspard, Kabalan, Gaspard, Kabalan,
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Explicit Reciprocity Laws In Algebraic Function Fields (cyclotomic, Kummer).
, 1987 Let IF(,q) denote the finite field with q elements where q = p('r) is a power of an odd prime p, IF(,q) x the polynomial ring in one indeter- minate x with coefficients in IF(,q), and IF(,q)(x) the field of rational functions in one indeterminate x with
Schultheis, Fred Bentley
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A P‐adic class formula for Anderson t‐modules
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In 2012, Taelman proved a class formula for L$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$‐modules.
Alexis Lucas
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Sparse Representation for Cyclotomic Fields [PDF]
Experimental Mathematics, 2007 Currently, all major implementations of cyclotomic fields as well as number fields are based on a dense model in which elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed basis. While this representation allows for the asymptotically fastest arithmetic for general elements,
openaire +2 more sources
Ordinary primes for GL2$\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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Remarks on the Coefficients of Inverse Cyclotomic Polynomials
, 2023 Cyclotomic polynomials play an imporant role in discrete mathematics. Recently, inverse cyclotomic polynomials have been defined and investigated.
Andrica, D. +2 more
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