Results 61 to 70 of about 11,330 (177)

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

Unifying error-correcting code/Narain CFT correspondences via lattices over integers of cyclotomic fields

Physics Letters B
We 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
doaj   +1 more source

On the density of cyclotomic lattices constructed from codes

, 2016
Recently, Venkatesh improved the best known lower bound for lattice sphere packings by a factor $\log\log n$ for infinitely many dimensions $n$. Here we prove an effective version of this result, in the sense that we exhibit, for the same set of ...
Moustrou, Philippe
core   +3 more sources

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

On Integral Representations over Cyclotomic Fields

Journal of Number Theory, 1996
The following generalization of the second author's thesis [\textit{O. Neiße}, Augsburger Mathematisch-Naturwissenschaftliche Schriften. 3 (Wißner Verlag, 1995; Zbl 0826.20004)] is proved: Let \(G\) be a finite solvable group and \(\chi\) an irreducible complex character of \(G\) with odd degree.
Cram, Georg-Martin, Neiße, Olaf
openaire   +2 more sources

A probabilistic approach to value sets of polynomials over finite fields [PDF]

, 2014
In this paper we study the distribution of the size of the value set for a random polynomial with degree at most $q-1$ over a finite field $\mathbb{F}_q$.
Gao, Zhicheng, Wang, Qiang
core  

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

Parity of ranks of Jacobians of curves

Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.
Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser, Holly Green, Alexandros Konstantinou, Adam Morgan   +3 more
wiley   +1 more source

The Iwasawa invariants of Zpd${\mathbb {Z}}_{p}^{\,d}$‐covers of links

Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.
Abstract Let p$p$ be a prime number and let d∈Z>0$d\in {\mathbb {Z}}_{>0}$. In this paper, following the analogy between knots and primes, we study the p$p$‐torsion growth in a compatible system of (Z/pnZ)d$({\mathbb {Z}}/p^n{\mathbb {Z}})^d$‐covers of 3‐manifolds and establish several analogues of Cuoco–Monsky's multivariable versions of Iwasawa's ...
Sohei Tateno, Jun Ueki
wiley   +1 more source