1 citations · 1 across the 4 of their papers we have counts for
6 papers
On the factorization of twisted -values and -descents over -number fields
Céline Maistret, Himanshu Shukla
We investigate the Galois module structure of the Tate-Shafarevich group of elliptic curves. For a Dirichlet character , we give an explicit conjecture relating the ideal factor…
Towards a classification of isolated -invariants
Abbey Bourdon, Sachi Hashimoto, Timo Keller +5
We develop an algorithm to test whether a non-CM elliptic curve gives rise to an isolated point of any degree on any modular curve of the form . This builds…
The Cassels-Tate pairing on 2-Selmer groups of elliptic curves
Himanshu Shukla, Michael Stoll
We explicitly compute the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve using the Albanese-Albanese definition of the pairing given by Poonen and Stoll. This lead…
How many zeros of a random sparse polynomial are real?
Gorav Jindal, Anurag Pandey, Himanshu Shukla +1
We investigate the number of real zeros of a univariate -sparse polynomial over the reals, when the coefficients of come from independent standard normal distributions.…
Definable combinatorics with dense linear orders
Himanshu Shukla, Arihant Jain, Amit Kuber
We compute the model-theoretic Grothendieck ring, , of a dense linear order (DLO) with or without end points, , as a structure of the signature…
On Resource-bounded versions of the van Lambalgen theorem
Diptarka Chakraborty, Satyadev Nandakumar, Himanshu Shukla
The van Lambalgen theorem is a surprising result in algorithmic information theory concerning the symmetry of relative randomness. It establishes that for any pair of infinite sequ…