29 citations · 80 across the 13 of their papers we have counts for
14 papers
Counting number fields of fixed degree by their smallest defining polynomial
Santiago Arango-Piñeros, Fabian Gundlach, Robert J. Lemke Oliver +5
When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of on the space of polynom…
Malle's Conjecture for Galois octic fields over
Arul Shankar, Ila Varma
We compute the asymptotic number of octic number fields whose Galois groups over are isomorphic to , the symmetries of a square, when ordering such fields by their…
Power-saving error terms for the number of -quartic extensions over a number field ordered by discriminant
Alina Bucur, Alexandra Florea, Allechar Serrano López +1
We study the asymptotic count of dihedral quartic extensions over a fixed number field with bounded norm of the relative discriminant. The main term of this count (including a summ…
Geometry-of-numbers methods in the cusp
Arul Shankar, Artane Siad, Ashvin Swaminathan +1
In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We il…
On unit signatures and narrow class groups of odd degree abelian number fields
Benjamin Breen, Ila Varma, John Voight +1
For an abelian number field of odd degree, we study the structure of its 2-Selmer group as a bilinear space and as a Galois module. We prove structural results and make predictions…
The number of quartic -fields ordered by conductor
Salim Ali Altug, Arul Shankar, Ila Varma +1
We consider families of number fields of degree 4 whose normal closures over have Galois group isomorphic to , the symmetries of a square. To any such field ,…
The mean number of 3-torsion elements in ray class groups of quadratic fields
Ila Varma
We determine the average number of -torsion elements in the ray class groups of fixed (integral) conductor of quadratic fields ordered by absolute discriminant, generalizing…
Odd degree number fields with odd class number
Wei Ho, Arul Shankar, Ila Varma
For every odd integer , we prove that there exist infinitely many number fields of degree and associated Galois group whose class number is odd. To do so, we st…
Differential operators and families of automorphic forms on unitary groups of arbitrary signature
Ellen Eischen, Jessica Fintzen, Elena Mantovan +1
In the 1970's, Serre exploited congruences between -expansion coefficients of Eisenstein series to produce -adic families of Eisenstein series and, in turn, -adic zeta fun…
Local-global compatibility for regular algebraic cuspidal automorphic representation when
Ila Varma
We prove the compatibility of local and global Langlands correspondences for up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne…
p-adic q-expansion principles on unitary Shimura varieties
Ana Caraiani, Ellen Eischen, Jessica Fintzen +2
We formulate and prove certain vanishing theorems for p-adic automorphic forms on unitary groups of arbitrary signature. The p-adic q-expansion principle for p-adic modular forms o…
On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields
Manjul Bhargava, Ila Varma
Given any family of cubic fields defined by local conditions at finitely many primes, we determine the mean number of 2-torsion elements in the class groups and narrow class groups…
The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders
Manjul Bhargava, Ila Varma
We determine the mean number of 3-torsion elements in the class groups of quadratic orders, where the quadratic orders are ordered by their absolute discriminants. Moreover, for a…
Finding elementary formulas for theta functions associated to even sums of squares
Ila Varma
This article discusses the classical problem of how to calculate , the number of ways to represent an integer by a sum of squares from a computational efficiency vi…