Results 61 to 70 of about 4,688 (128)

A Density of Ramified Primes. [PDF]

Res Number Theory, 2022
Chan S, McMeekin C, Milovic D.
europepmc   +1 more source

On the structure of the Galois group of the maximal pro-$p$ extension with restricted ramification over the cyclotomic $\mathbb{Z}_p$-extension

, 2018
Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of an algebraic number field $k$. We denote by $S$ a finite set of prime numbers which does not contain $p$, and $S(k_\infty)$ the set of primes of $k_\infty$ lying above $S$. In the present paper,
Itoh, Tsuyoshi
core  

Another look at rational torsion of modular Jacobians. [PDF]

Proc Natl Acad Sci U S A, 2022
Ribet KA, Wake P.
europepmc   +1 more source

cuSCNN: A Secure and Batch-Processing Framework for Privacy-Preserving Convolutional Neural Network Prediction on GPU. [PDF]

Front Comput Neurosci, 2021
Bai Y, Liu Q, Wu W, Feng Y.
europepmc   +1 more source

On some determinants involving cyclotomic units

, 2019
For each odd prime $p$, let $ _p$ denote a primitive $p$-th root of unity. In this paper, we study the determinants of some matrices with cyclotomic unit entries. For instance, we show that when $p\equiv 3\pmod4$ and $p>3$ the determinant of the matrix $\(\frac{1- _p^{j^2k^2}}{1- _p^{j^2}}\)_{1\le j,k\le (p-1)/2}$ can be written as $(-1)^{\frac{h(
openaire   +2 more sources

On the Orthogonal of Cyclotomic Units in Positive Characteristic

Journal of Number Theory, 1999
This is a very interesting and powerful piece of mathematics. Let \(A:= \mathbb{F}_q[T]\) where \(\mathbb{F}_q\) is the finite field of \(q=p^m\) elements. Let \(P\in A\) be a monic prime of degree \(d\). In work by the author [J. Number Theory 78, 228-252 (1999; Zbl 0937.11020)] and \textit{F. Schultheis} [J.
openaire   +1 more source

On a cyclotomic unit and related products

Journal of Number Theory, 1991
AbstractLet p be an odd prime, ζ a primitive pth root of unity. It is proved that Π(1 + iζk)k, 1 ≤ k ≤ p − 1 is a perfect pth power in Z(iζ) only if p divides Σtp − 3, 1 ≤ t ≤ ⌊p4⌋, and that it is a perfect pth power for P = 241. Properties of the general product Π(1 + aqk)k, 1 ≤ k ≤ n, are investigated.
openaire   +1 more source

Cyclotomic Units in Zp-Extensions

Journal of Algebra, 1995
Kucera, R., Nekovar, J.
openaire   +1 more source

Adjoint modular Galois representations and their Selmer groups. [PDF]

Proc Natl Acad Sci U S A, 1997
Hida H, Tilouine J, Urban E.
europepmc   +1 more source

The Eisenstein ideal at prime-square level has constant rank. [PDF]

Proc Natl Acad Sci U S A
Lang J, Wake P.
europepmc   +1 more source