Results 41 to 50 of about 160 (151)

Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])$\operatorname{GL}_2(\mathbb {F}_q[T])$

Mathematika, Volume 72, Issue 2, April 2026.
Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley   +1 more source

On families of K3 surfaces with real multiplication

Forum of Mathematics, Sigma
We exhibit large families of K3 surfaces with real multiplication, both abstractly, using lattice theory, the Torelli theorem and the surjectivity of the period map, as well as explicitly, using dihedral covers and isogenies.
Bert van Geemen, Matthias Schütt
doaj   +1 more source

Dual Isogenies and Their Application to Public-Key Compression for Isogeny-Based Cryptography

, 2019
The isogeny-based protocols SIDH and SIKE have received much attention for being post-quantum key agreement candidates that retain relatively small keys. A recent line of work has proposed and further improved compression of public keys, leading to the inclusion of public-key compression in the SIKE proposal for Round 2 of the NIST Post-Quantum ...
Naehrig, M., Renes, J.
openaire   +3 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
wiley   +1 more source

Constant time lattice reduction in dimension 4 with application to SQIsign

Transactions on Cryptographic Hardware and Embedded Systems
In this paper we propose a constant time lattice reduction algorithm for integral dimension-4 lattices. Motivated by its application in the SQIsign postquantum signature scheme, we provide for the first time a constant time LLLlike algorithm with ...
Otto Hanyecz, Alexander Karenin, Elena Kirshanova, Péter Kutas, Sina Schaeffler   +4 more
doaj   +1 more source

Renormalization, Isogenies, and Rational Symmetries of Differential Equations

Advances in Mathematical Physics, 2010
We give an example of infinite-order rational transformation that leaves a linear differential equation covariant. This example can be seen as a nontrivial but still simple illustration of an exact representation of the renormalization group.
A. Bostan, S. Boukraa, S. Hassani, J.-M. Maillard, J.-A. Weil, N. Zenine, N. Abarenkova   +6 more
doaj   +1 more source

Graph potentials and topological quantum field theories

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
wiley   +1 more source

On the Parallelization of Square-Root Vélu’s Formulas

Mathematical and Computational Applications
A primary challenge in isogeny-based cryptography lies in the substantial computational cost associated to computing and evaluating prime-degree isogenies.
Jorge Chávez-Saab, Odalis Ortega, Amalia Pizarro-Madariaga   +2 more
doaj   +1 more source

Vector bundles on bielliptic surfaces: Ulrich bundles and degree of irrationality

Mathematische Nachrichten, Volume 299, Issue 3, Page 514-528, March 2026.
Abstract This paper deals with two problems about vector bundles on bielliptic surfaces. The first is to give a classification of Ulrich bundles on such surfaces S$S$, which depends on the topological type of S$S$. In doing so, we study the weak Brill–Noether property for moduli spaces of sheaves with isotropic Mukai vector. Adapting an idea of Moretti
Edoardo Mason
wiley   +1 more source

On the Euler characteristic of S$S$‐arithmetic groups

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We show that the sign of the Euler characteristic of an S$S$‐arithmetic subgroup of a simple algebraic group depends on the S$S$‐congruence completion only, except possibly in type 6D4${}^6 D_4$. Consequently, the sign is a profinite invariant for such S$S$‐arithmetic groups with the congruence subgroup property. This generalizes previous work
Holger Kammeyer, Giada Serafini
wiley   +1 more source