Results 61 to 70 of about 545 (160)

Cyclotomic Classes in a Product of Finite Abelian Groups and Applications

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Cyclotomic classes of finite abelian groups have been extensively investigated for many decades, largely because of their nice algebraic structure and the breadth of their theoretical and practical applications. They naturally arise in diverse areas of mathematics, ranging from number theory and polynomial factorization to the decomposition of group ...
Somphong Jitman, Faranak Farshadifar
wiley   +1 more source

A Construction of Binary Cyclotomic Sequences Using Extension Fields

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2009
Based on the cyclotomy classes of extension fields, a family of binary cyclotomic sequences are constructed and their pseudorandom measures (i.e., the well-distribution measure and the correlation measure of order k) are estimated using certain exponential sums.
CHEN, Zhixiong, DU, Xiaoni, SUN, Rong
openaire   +1 more source

Chebotarev's theorem for cyclic groups of order pq$pq$ and an uncertainty principle

Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3841-3856, December 2025.
Abstract Let p$p$ be a prime number and ζp$\zeta _p$ a primitive p$p$th root of unity. Chebotarev's theorem states that every square submatrix of the p×p$p \times p$ matrix (ζpij)i,j=0p−1$(\zeta _p^{ij})_{i,j=0}^{p-1}$ is nonsingular. In this paper, we prove the same for principal submatrices of (ζnij)i,j=0n−1$(\zeta _n^{ij})_{i,j=0}^{n-1}$, when n=pr ...
Maria Loukaki
wiley   +1 more source

Real Belyi theory [PDF]

, 2007
We develop a Belyi type theory that applies to Klein surfaces, i.e. (possibly non-orientable) surfaces with boundary which carry a dianalytic structure.
Koeck, Bernhard, Singerman, David
core   +1 more source

The m$m$‐step solvable anabelian geometry of mixed‐characteristic local fields

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract Let K$K$ be a mixed‐characteristic local field. For an integer m⩾0$m \geqslant 0$, we denote by Km/K$K^m / K$ the maximal m$m$‐step solvable extension of K$K$, and by GKm$G_K^m$ the maximal m$m$‐step solvable quotient of the absolute Galois group GK$G_K$ of K$K$.
Seung‐Hyeon Hyeon
wiley   +1 more source

On the Iwasawa 𝜆-invariant of the cyclotomic ℤ₂-extension of ℚ(√𝕡) [PDF]

Mathematics of Computation, 2009
We study the Iwasawa λ \lambda ...
Takashi Fukuda, Keiichi Komatsu
openaire   +1 more source

General Gate Teleportation and the Inner Structure of Its Clifford Hierarchies

Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15985-15997, 30 November 2025.
ABSTRACT The quantum gate teleportation mechanism allows for the fault‐tolerant implementation of “Clifford hierarchies” of gates assuming, among other things, a fault‐tolerant implementation of the Pauli gates. We discuss how this method can be extended to assume the fault‐tolerant implementation of any orthogonal unitary basis of operators, in such a
Samuel González‐Castillo, Elías F. Combarro, Ignacio F. Rúa, José Ranilla   +3 more
wiley   +1 more source

Growth problems in diagram categories

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3454-3469, November 2025.
Abstract In the semisimple case, we derive (asymptotic) formulas for the growth rate of the number of summands in tensor powers of the generating object in diagram/interpolation categories.
Jonathan Gruber, Daniel Tubbenhauer
wiley   +1 more source

The geometry and arithmetic of bielliptic Picard curves

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley   +1 more source

A note on local formulae for the parity of Selmer ranks

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3112-3132, October 2025.
Abstract In this note, we provide evidence for a certain ‘twisted’ version of the parity conjecture for Jacobians, introduced in prior work of Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p∞$p^\infty$‐Selmer groups.
Adam Morgan
wiley   +1 more source