Results 41 to 50 of about 545 (160)
Lower bounds for heights in cyclotomic extensions
Journal of Number Theory, 2010 Let \(f(x) = a_{0} \prod_{i=1}^{d} (x-\alpha_{i}) = a_{0}x^{n}+a_{1}x^{n-1}+ \cdots + a_{n}\) be an irreducible polynomial with integer coefficients. The Mahler measure of \(f\) is defined to be \(M(f) =\prod_{i=1}^{d}\max \{ 1, |\alpha_{i}| \}\). If \(\alpha \neq 0\) is a root of \(f\), then the absolute logarithmic height \(h(\alpha)\) of \(\alpha ...
Ishak, M.I.M. +3 more
openaire +2 more sources
Sylow subgroups and the number of irreducible characters of degrees divisible by a prime p$p$
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let G$G$ be a finite group and p$p$ be a prime. We establish an upper bound for the derived length of a Sylow p$p$‐subgroup of G$G$ in terms of the number of irreducible characters of G$G$ whose degrees are divisible by p$p$. We also prove that if B$B$ is a p$p$‐block of a finite p$p$‐solvable group G$G$ with defect group D$D$, then the ...
James P. Cossey +3 more
wiley +1 more source
Projective modules of group rings over quadratic number fields [PDF]
, 1994 Let K be a quadratic number field, Ok its ring of integers, and G a cyclic group of order prime p. In this thesis, we study the kernel group D(O(_K)G) and obtain a number of results concerning its order and structure. For K imaginary, we also investigate
Ahmed, Iftikhar
core
Iwasawa theory for modular forms at supersingular primes
, 2010 Let f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q.
Antonio Lei
core +1 more source
RANKS OF p-CLASS GROUPS IN CYCLIC p-EXTENSIONS OF ANTI-CYCLOTOMIC Z2-EXTENSIONS [PDF]
, 2019 In [1], Iwasawa proved a structure theorem for the l-class group in Zl-extensions. In this thesis, we consider instead the p-class group in Zl-extensions, particularly when l=2 and p=3. Fixing K0 =Q(i), we let L0/K0 be a cyclic degree p extension and let
Kirsch, Ariella
core +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
Normal high order elements in finite field extensions based on the cyclotomic polynomials
, 2020 We consider elements which are both of high multiplicative order and normal in extensions Fqm of the field Fq. If the extension is defined by a cyclotomic polynomial, we construct such elements explicitly and give explicit lower bounds on their orders ...
Skuratovskii, R., Popovych, R.
core +1 more source
Motivic mirror symmetry and χ$\chi$‐independence for Higgs bundles in arbitrary characteristic
Proceedings of the London Mathematical Society, Volume 132, Issue 6, June 2026.Abstract We prove that the (twisted orbifold) motives of the moduli spaces of SLn$\mathrm{SL}_n$ and PGLn$\mathrm{PGL}_n$‐Higgs bundles of coprime rank and degree on a smooth projective curve over an algebraically closed field in which the rank is invertible are isomorphic in Voevodsky's triangulated category of motives.
Victoria Hoskins, Simon Pepin Lehalleur
wiley +1 more source
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 +3 more
wiley +1 more source
Engineering Reports, Volume 8, Issue 4, April 2026.Smart meter (SM): Collect the data of users' electricity consumption periodically, and preprocess the noise reduction by using the Robust Local Weighted Regression algorithm, then encrypt the private data in it by Boneh‐Goh‐Nissim homomorphic encryption, and submit the encrypted private data to the fog node.
Jiangtao Guo +5 more
wiley +1 more source