Results 31 to 40 of about 6,424 (109)

On Functions of $\mathbb{F}_{2^{2t}}$ mapping Cosets of $\mathbb{F}_{2^{t}}^{*}$ to Cosets of $\mathbb{F}_{2^{t}}^{*}$

International audienceThe punctured finite field $\mathbb{F}_{2^{2t}}^*$ can be partitioned into multiplicative cosets of $\mathbb{F}_{2^{t}}^*$.In this paper, we investigate functions mapping these cosets either to multiplicative cosets of $\mathbb{F}_ ...
Perrin, Léo, Baudrin, Jules, Canteaut, Anne   +2 more
core   +4 more sources

A trace–path integral formula over function fields

Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.
Abstract We show that an arithmetic path integral over the ℓ$\ell$‐torsion of a Jacobian J[ℓ]$J[\ell]$ is equal to the trace of the Frobenius action on a representation of the Heisenberg group H(J[ℓ])$H(J[\ell])$, up to an explicitly determined sign.
Yan Yau Cheng
wiley   +1 more source

The asymptotic Mahler measure of Gaussian periods

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract We construct a sequence of cyclotomic integers (Gaussian periods) of particularly small Mahler measure/height. We study the asymptotics of their Mahler measure as a function of their conductor, to find that the growth rate is the (multivariate) Mahler measure of a family of log Calabi–Yau varieties of increasing dimension.
Gunther Cornelissen, David Hokken, Berend Ringeling   +2 more
wiley   +1 more source

On constructing bent functions from cyclotomic mappings

, 2023
We study a new method of constructing Boolean bent functions from cyclotomic mappings. Three generic constructions are obtained by considering different branch functions such as Dillon functions, Niho functions and Kasami functions over multiplicative ...
Wang, Qiang, Xie, Xi, Li, Nian, Zeng, Xiangyong   +3 more
core  

The Multiple Equal-Difference Structure of Cyclotomic Cosets

CoRR
In this paper we introduce the definition of equal-difference cyclotomic coset, and prove that in general any cyclotomic coset can be decomposed into a disjoint union of equal-difference subsets. Among the equal-difference decompositions of a cyclotomic coset, an important class consists of those in the form of cyclotomic decompositions, called the ...
Li Zhu, Juncheng Zhou, Jinle Liu, Hongfeng Wu   +3 more
openaire   +2 more sources

Cpn$C_{p^n}$‐equivariant Mahowald invariants

Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.
Abstract The classical Mahowald invariant is an operation that systematically produces new elements in the stable homotopy groups of spheres from known ones. We introduce the Cpn$C_{p^n}$‐Mahowald invariant: a relation π★SCpn−1⇀π*S$\pi _\star S_{\mathchoice{{ C_{p^{n-1}}}}{{\textstyle C_{p^{n-1}}}}{{\scriptstyle C_{p^{n-1}}}}{{\scriptscriptstyle C_{p ...
William Balderrama, Yueshi Hou, Shangjie Zhang   +2 more
wiley   +1 more source

A Closed-Form Hamming-Weight Variance Formula for Cyclic LCD Codes in Orthogonal Direct Sum Masking

Cryptography
Orthogonal direct sum masking (ODSM) protects embedded cryptographic implementations against side-channel attacks by splitting the ambient space into a source code C carrying sensitive data and a complementary masking code D carrying fresh randomness ...
Guillermo Sosa-Gómez
doaj   +1 more source

On the Lang–Trotter conjecture for Siegel modular forms

Mathematika, Volume 72, Issue 3, July 2026.
Abstract Let f$f$ be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with f$f$, generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues ap$a_p$ of f$f$, and obtain upper
Arvind Kumar, Moni Kumari, Ariel Weiss
wiley   +1 more source

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

p$p$‐adic equidistribution and an application to S$S$‐units

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We prove a Galois equidistribution result for torsion points in Gmn$\mathbb {G}_m^n$ in the p$p$‐adic setting for test functions of the form log|F|p$\log |F|_p$ where F$F$ is a nonzero polynomial with coefficients in the field of complex p$p$‐adic numbers.
Gerold Schefer
wiley   +1 more source