1 citations · 3 across the 14 of their papers we have counts for
16 papers
The existence of small defining polynomials for number fields
Manjul Bhargava, Sameera Vemulapalli
We prove that every number field of degree and absolute discriminant has a defining integral polynomial of degree whose coefficients are all in size, thu…
Local Factors in the BSD Conjecture: A Unified Statistical View
David Kurniadi Angdinata, Kenny Lau, Ken Ono +2
For elliptic curves in short Weierstrass form \[ E=E(a_4,a_6): y^2=x^3+a_4x+a_6, \] we derive a multivariable Euler product generating function which encodes the Tam…
Tschirnhausen bundles of sextic covers of
Sam Frengley, Sameera Vemulapalli
A degree genus cover of the complex projective line by a smooth irreducible curve yields a vector bundle on the projective line by pushforward of the structure sheaf. W…
Tschirnhausen Bundles of Quintic Covers of
Sam Frengley, Sameera Vemulapalli
A degree genus cover of the complex projective line by a smooth irreducible curve yields a vector bundle on the projective line by pushforward of the structure sheaf. W…
Unit lattices of -quartic number fields with signature
Sergio Ricardo Zapata Ceballos, Sara Chari, Erik Holmes +5
There has been a recent surge of interest on distributions of shapes of unit lattices in number fields, due to both their applications to number theory and the lack of known result…
Galois groups of simple abelian varieties over finite fields and exceptional Tate classes
Santiago Arango-Piñeros, Sam Frengley, Sameera Vemulapalli
We prove new cases of the Tate conjecture for abelian varieties over finite fields, extending previous results of Dupuy--Kedlaya--Zureick-Brown, Lenstra--Zarhin, Tankeev, and Zarhi…
Shapes of unit lattices in -number fields
Robert Harron, Erik Holmes, Sameera Vemulapalli
The unit group of the ring of integers of a number field, modulo torsion, is a lattice via the logarithmic Minkowski embedding. We examine the shape of this lattice, which we call…
Galois groups of low dimensional abelian varieties over finite fields
Santiago Arango-Piñeros, Sam Frengley, Sameera Vemulapalli
We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick…
Brill--Noether theory of smooth curves in the plane and on Hirzebruch surfaces
Hannah Larson, Sameera Vemulapalli
In this paper, we describe the Brill--Noether theory of a general smooth plane curve and a general curve on a Hirzebruch surface of fixed class. It is natural to study the line…
The Steinitz Realization Problem
Sameera Vemulapalli
Let be a number field and let . The Steinitz realization problem asks: does every element of the ideal class group of occur as the Steinitz class of…
The distribution of lattices arising from orders in low degree number fields
Sameera Vemulapalli
Orders in number fields provide natural examples of lattices. We ask: what can the successive minima of lattices arising from orders in number fields be? Given an order $\mathcal{O…
Sumsets of sequences in abelian groups and flags in field extensions
Sameera Vemulapalli
For a finite abelian group with subsets and , the sumset is . A fundamental problem in additive combinatorics is to find a lower bound…
Bounds on Successive Minima of Orders in Number Fields and Scrollar Invariants of Curves
Sameera Vemulapalli
Orders and fractional ideals in number fields provide interesting examples of lattices. We ask: what lattices arise from orders in number fields? We prove that all nontrivial multi…
On intersections of symmetric determinantal varieties and theta characteristics of canonical curves
Avinash Kulkarni, Sameera Vemulapalli
From a block-diagonal tensor symmetric in the last two entries one obtains two varieties: an intersection of symmetric determinantal hypersurfaces…
Computing Unit Groups of Curves
Justin Chen, Sameera Vemulapalli, Leon Zhang
The group of units modulo constants of an affine variety over an algebraically closed field is free abelian of finite rank. Computing this group is difficult but of fundamental imp…
Uniform Bounds for the Number of Rational Points on Symmetric Squares of Curves with Low Mordell-Weil Rank
Sameera Vemulapalli, Danielle Wang
A central problem in Diophantine geometry is to uniformly bound the number of -rational points on a smooth curve in terms of and its genus . A recent paper by Stoll…