Results 51 to 60 of about 9,407 (175)

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

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

Unitary cyclotomic polynomials

, 2019
The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials. We formulate some basic properties of unitary cyclotomic polynomials and study how they are connected with cyclotomic, inclusion-exclusion and Kronecker polynomials.
Moree, Pieter, Tóth, László
openaire   +4 more sources

Feasibility of primality in bounded arithmetic

Forum of Mathematics, Sigma
We prove the correctness of the AKS algorithm [1] within the bounded arithmetic theory $T^{\text {count}}_2$ or, equivalently, the first-order consequences of the theory $\text {VTC}^0$ expanded by the smash function, which we denote by
Raheleh Jalali, Ondřej Ježil
doaj   +1 more source

Sister Beiter and Kloosterman: a tale of cyclotomic coefficients and modular inverses [PDF]

, 2012
For a fixed prime $p$, the maximum coefficient (in absolute value) $M(p)$ of the cyclotomic polynomial $\Phi_{pqr}(x)$, where $r$ and $q$ are free primes satisfying $r>q>p$ exists. Sister Beiter conjectured in 1968 that $M(p)\le(p+1)/2$.
Cobeli, Cristian, Gallot, Yves, Moree, Pieter, Zaharescu, Alexandru   +3 more
core  

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

The growth of Tate–Shafarevich groups of p$p$‐supersingular elliptic curves over anticyclotomic Zp${\mathbb {Z}}_p$‐extensions at inert primes

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Let E$E$ be an elliptic curve defined over Q${\mathbb {Q}}$, and let K$K$ be an imaginary quadratic field. Consider an odd prime p$p$ at which E$E$ has good supersingular reduction with ap(E)=0$a_p(E)=0$ and which is inert in K$K$. Under the assumption that the signed Selmer groups are cotorsion modules over the corresponding Iwasawa algebra ...
Erman Işik, Antonio Lei
wiley   +1 more source

Counting primes with a given primitive root, uniformly

Mathematika, Volume 71, Issue 4, October 2025.
Abstract The celebrated Artin conjecture on primitive roots asserts that given any integer g$g$ that is neither −1$-1$ nor a perfect square, there is an explicit constant A(g)>0$A(g)>0$ such that the number Π(x;g)$\Pi (x;g)$ of primes p⩽x$p\leqslant x$ for which g$g$ is a primitive root is asymptotically A(g)π(x)$A(g)\pi (x)$ as x→∞$x\rightarrow \infty$
Kai (Steve) Fan, Paul Pollack
wiley   +1 more source

Wild blocks of type A$A$ Hecke algebras are strictly wild

Bulletin of the London Mathematical Society, Volume 57, Issue 9, Page 2658-2679, September 2025.
Abstract We prove that all wild blocks of type A$A$ Hecke algebras with quantum characteristic e⩾3$e \geqslant 3$ — that is, blocks of weight at least 2 — are strictly wild, with the possible exception of the weight 2 Rouquier block for e=3$e = 3$.
Liron Speyer
wiley   +1 more source