12 citations · 54 across the 13 of their papers we have counts for
14 papers
The ring of finite algebraic numbers and its application to the law of decomposition of primes
Julian Rosen, Yoshihiro Takeyama, Koji Tasaka +1
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give ap…
The moduli space of -algebras
Andrew O'Desky, Julian Rosen
Let be a Galois algebra with Galois group and let be a normal element of . The moduli space of pairs is isomorphic to an open subset of the quot…
A finite analogue of the ring of algebraic numbers
Julian Rosen
We construct an analogue of the ring of algebraic numbers, living in a quotient of the product of all finite fields of prime order. We use this ring to deduce some results about li…
Sequential periods of the crystalline Frobenius
Julian Rosen
There is a notion of -adic period coming from the crystalline Frobenius automorphism of the de Rham cohomology of an algebraic variety. In this paper, we consider sequences of $…
A choice-free absolute Galois group and Artin motives
Julian Rosen
Proofs that an arbitrary field has a separable closure are necessarily non-constructive, and separable closures are unique only up to non-canonical isomorphism. This means that the…
A general family of congruences for Bernoulli numbers
Julian Rosen
We prove a general family of congruences for Bernoulli numbers whose index is a polynomial function of a prime, modulo a power of that prime. Our family generalizes many known resu…