F. Hajir

activity

20012026

most citedGenerating Functions, Polynomials and Vortices with Alternating Signs in Bose-Einstein Condensates

46 citations · 83 across the 17 of their papers we have counts for

collaborators

20 papers

math.NT2026

Hasse-Witt invariants for trace forms of Jacobi polynomials

John Cullinan, Farshid Hajir, Elisabeth Young

In \cite{feit}, Feit used the Generalized Laguerre Polynomials (GLP) to prove that the groups $A_{5}$ and $A_{7}$ occur as Galois groups over $\Q$. Hajir, i…

math.NT2024

On tamely ramified infinite Galois extensions

Farshid Hajir, Michael Larsen, Christian Maire +1

For a number field $K$ , we consider $K^{ta}$ the maximal tamely ramified algebraic extension of~ $K$ , and its Galois group $G_{K}^{ta} = G a l (K^{t a} / K)$ . Choose a prime $p$ such…

math.NT2022

On tame $Z / p Z$ extensions with prescribed ramification

Farshid Hajir, Christian Maire, Ravi Ramakrishna

The tame Gras-Munnier Theorem gives a criterion for the existence of a $Z / Z$ -extension of a number field $K$ ramified at exactly a set $S$ of places of $K$ prim…

math.NT2022★ 1 cited

On Ozaki's theorem realizing prescribed $p$ -groups as $p$ -class tower groups

Farshid Hajir, Christian Maire, Ravi Ramakrishna

We give a streamlined and effective proof of Ozaki's theorem that any finite $p$ -group $Γ$ is the Galois group of the $p$ -Hilbert class field tower of some number field $F$ . Ou…

math.NT2021★ 1 cited

Deficiency of p-Class Tower Groups and Minkowski Units

Farshid Hajir, Christian Maire, Ravi Ramakrishna

Let $p$ be a prime. We define the deficiency of a finitely-generated pro- $p$ group $G$ to be $r (G) - d (G)$ where $d (G)$ is the minimal number of generators of $G$ and $r (G)$ is its m…

math.NT2019

On the Shafarevich Group of Restricted Ramification Extensions of Number Fields in the Tame Case

Farshid Hajir, Christian Maire, Ravi Ramakrishna

Let $K$ be a number field and $S$ a finite set of places of $K$ . We study the kernels $\Sha_S$ of maps $H^2(G_S,\fq_p) \rightarrow \oplus_{v\in S} H^2(\G_v,\fq_p)$. There is a natu…

Hasse-Witt invariants for trace forms of Jacobi polynomials

On tamely ramified infinite Galois extensions

On tame Z/pZ extensions with prescribed ramification

On Ozaki's theorem realizing prescribed p-groups as p-class tower groups

Deficiency of p-Class Tower Groups and Minkowski Units

On the Shafarevich Group of Restricted Ramification Extensions of Number Fields in the Tame Case

On tame $Z / p Z$ extensions with prescribed ramification

On Ozaki's theorem realizing prescribed $p$ -groups as $p$ -class tower groups