Ravi Ramakrishna

activity

20002025

most citedSome supercongruences occurring in truncated hypergeometric series

8 citations · 22 across the 13 of their papers we have counts for

collaborators

16 papers

math.NT2025

Increasing the Size of Tame Shafarevich Groups

Andreea Iorga, Ravi Ramakrishna

Let $K$ be a number field with $S$ a finite set of primes. We study the cohomology of $F_{p} [G_{K, S}]$ -modules $A$ , in particular the Shafarevich groups $\Sha^i_S(K,A)$ for…

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★ 4 cited

Quantitative level lowering for Galois representations

Najmuddin Fakhruddin, Chandrashekhar Khare, Ravi Ramakrishna

We use Galois cohomology methods to produce optimal mod $p^{d}$ level lowering congruences to a $p$ -adic Galois representation that we construct as a well chosen lift of a given resi…

Increasing the Size of Tame Shafarevich Groups

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

Quantitative level lowering for Galois representations

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

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