1 citations · 3 across the 14 of their papers we have counts for
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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…
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…
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…
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…