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For each odd prime $p$, we conjecture the distribution of the $p$-torsion subgroup of $K_{2n}(mathcal{O}_F)$ as $F$ ranges over real quadratic fields, or over imaginary quadratic fields. We then prove that the average size of the $3$-torsion subgroup of $K_{2n}(mathcal{O}_F)$ is as predicted by this conjecture.
We compute the etale cohomology ring $H^*(text{Spec } mathcal{O}_K,mathbb{Z}/nmathbb{Z})$ where $mathcal{O}_K$ is the ring of integers of a number field $K.$ As an application, we give a non-vanishing formula for an invariant defined by Minhyong Kim.
We present a variation of the modular algorithm for computing the Hermite normal form of an $mathcal O_K$-module presented by Cohen, where $mathcal O_K$ is the ring of integers of a number field $K$. An approach presented in (Cohen 1996) based on red
Each p-ring class field K(f) modulo a p-admissible conductor f over a quadratic base field K with p-ring class rank r(f) mod f is classified according to Galois cohomology and differential principal factorization type of all members of its associated
One of the many number theoretic topics investigated by the ancient Greeks was perfect numbers, which are positive integers equal to the sum of their proper positive integral divisors. Mathematicians from Euclid to Euler investigated these mysterious
As an analogue of a link group, we consider the Galois group of the maximal pro-$p$-extension of a number field with restricted ramification which is cyclotomically ramified at $p$, i.e, tamely ramified over the intermediate cyclotomic $mathbb Z_p$-e