Results 71 to 80 of about 7,081,606 (216)

Counting 5‐isogenies of elliptic curves over Q$\mathbb {Q}$

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We show that the number of 5‐isogenies of elliptic curves defined over Q$\mathbb {Q}$ with naive height bounded by H>0$H > 0$ is asymptotic to C5·H1/6(logH)2$C_5\cdot H^{1/6} (\log H)^2$ for some explicitly computable constant C5>0$C_5 > 0$. This settles the asymptotic count of rational points on the genus zero modular curves X0(m)$\mathcal {X}
Santiago Arango‐Piñeros, Changho Han, Oana Padurariu, Sun Woo Park   +3 more
wiley   +1 more source

An integral formula for the coefficients of the inverse cyclotomic polynomial [PDF]

Some recent advances related to an integral formula for the coefficients of inverse cyclotomic polynomials, including applications and numerical simulations are ...
Andrica, D., Țurcaș, G. C., Bagdasar, O.   +2 more
core   +1 more source

On the linear complexity of a new generalized cyclotomic sequence with length ^mover GF(h)

Tongxin xuebao, 2017
Based on the Ding-generalized cyclotomy,a new class of generalized cyclotomic sequences with length pm over the finite field of power of odd prime order was constructed,and the sequence was balanced.The linear complexity of the sequences was determined ...
Long-fei LIU, Kai YANG, Xiao-yuan YANG
doaj   +2 more sources

A P‐adic class formula for Anderson t‐modules

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract In 2012, Taelman proved a class formula for L$L$‐series associated to Drinfeld Fq[θ]$\mathbb {F}_q[\theta]$‐modules and considered it as a function field analogue of the Birch and Swinnerton‐Dyer conjecture. Since then, Taelman's class formula has been generalized to the setting of Anderson t$t$‐modules.
Alexis Lucas
wiley   +1 more source

Efficient provable-secure NTRUEncrypt over any cyclotomic field [PDF]

, 2017
NTRUEncrypt is a fast lattice-based cryptosystem and a probable alternative of the existing public key schemes. The existing provable-secure NTRUEncrypts are limited by the cyclotomic field it works on - the prime-power cyclotomic field.
Mingqiang Wang, Yang Wang
core   +1 more source

Sparse Representation for Cyclotomic Fields [PDF]

Experimental Mathematics, 2007
Currently, all major implementations of cyclotomic fields as well as number fields are based on a dense model in which elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed basis. While this representation allows for the asymptotically fastest arithmetic for general elements,
openaire   +2 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

Class numbers of cyclotomic fields [PDF]

, 1985
In the first part of the paper we show how to construct real cyclotomic fields with large class numbers. If the GRH holds then the class number hp+ of the pth real cyclotomic field satisfies hp+ > p for the prime p = 11290018777.
Cornell, Gary, Lawrence C Washington, Washington, Lawrence C, Gary Cornell   +3 more
core   +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

Hypergeometric motives from Euler integral representations

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract We revisit certain one‐parameter families of affine covers arising naturally from Euler's integral representation of hypergeometric functions. We introduce a partial compactification of this family. We show that the zeta function of the fibers in the family can be written as an explicit product of L$L$‐series attached to nondegenerate ...
Tyler L. Kelly, John Voight
wiley   +1 more source