16 citations · 48 across the 25 of their papers we have counts for
22 papers · 1 filter
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…
Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks
Claudia Alfes, Ken Ono, Ashvin Swaminathan
When , the Dyson rank generating function is a classical bridge between partition theory, Ramanujan's mock theta functions, and the theory of harmonic Maass forms and nonhol…
On the Quartic Invariant of Odd Degree Binary Forms
Ashvin Swaminathan
We determine the squarefree part of the scalar factor that arises when the quartic invariant of the generic binary form of odd degree is expressed as the discriminant of…
The existence of infinitely many cubic fields with class group of exact 2-rank 1
Manjul Bhargava, Arul Shankar, Artane Siad +1
We show that infinitely many cubic fields have class group of 2-rank 1.
Parity of the partition function in quadratic progressions
Ken Ono, Ashvin Swaminathan
The parity of the partition function is one of the most stubborn problems in number theory. In 2010, the first author conjectured, for square-free , t…
A parametrization of -class groups of quadratic rings over Dedekind domains
Eliot Hodges, Ashvin A. Swaminathan
Let be a Dedekind domain with field of fractions and . In this paper, we generalize Bhargava's parametrization of -torsion ideal classes by…
The second moment of the size of the -class group of monogenized cubic fields
Manjul Bhargava, Arul Shankar, Ashvin Swaminathan
We prove that when totally real (resp., complex) monogenized cubic number fields are ordered by height, the second moment of the size of the -class group is at most (resp.,…
A positive proportion of monic odd-degree hyperelliptic curves of genus have no unexpected quadratic points
Jef Laga, Ashvin A. Swaminathan
Let be the family of monic odd-degree hyperelliptic curves of genus over . Poonen and Stoll have shown that for every , a positive proport…
Counting integral points on symmetric varieties with applications to arithmetic statistics
Arul Shankar, Artane Siad, Ashvin A. Swaminathan
In this article, we combine Bhargava's geometry-of-numbers methods with the dynamical point-counting methods of Eskin--McMullen and Benoist--Oh to develop a new technique for count…
The mean number of -torsion elements in the class groups of cubic orders
Ashvin Swaminathan
We determine the mean number of 2-torsion elements in class groups of cubic orders, when such orders are enumerated by discriminant. Specifically, we prove that when isomorphism cl…
The second moment of the size of the -Selmer group of elliptic curves
Manjul Bhargava, Arul Shankar, Ashvin Swaminathan
In this paper, we prove that when elliptic curves over are ordered by height, the second moment of the size of the -Selmer group is at most . This confirms a co…
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…
Hermite equivalence of polynomials
Manjul Bhargava, Jan-Hendrik Evertse, Kálmán Győry +2
In this paper, we resurrect a long-forgotten notion of equivalence for univariate polynomials with integral coefficients introduced by Hermite in the 1850s. We show that the Hermit…
A new parametrization for ideal classes in rings defined by binary forms, and applications
Ashvin Swaminathan
We give a parametrization of square roots of the ideal class of the inverse different of rings defined by binary forms in terms of the orbits of a coregular representation. This pa…
Most Odd-Degree Binary Forms Fail to Primitively Represent a Square
Ashvin Swaminathan
Let be a separable integral binary form of odd degree . A result of Darmon and Granville known as ``Faltings plus epsilon'' implies that the degree- \emph{superell…
Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of their Jacobians
Aaron Landesman, Ashvin Swaminathan, James Tao +1
In this article, we show that in each of four standard families of hyperelliptic curves, there is a density- subset of members with the property that their Jacobians have adelic…
Surjectivity of Galois Representations in Rational Families of Abelian Varieties
Aaron Landesman, Ashvin Swaminathan, James Tao +1
In this article, we show that for any non-isotrivial family of abelian varieties over a rational base with big monodromy, those members that have adelic Galois representation with…
Permutations that Destroy Arithmetic Progressions in Elementary -Groups
Noam D. Elkies, Ashvin Swaminathan
Given an abelian group , it is natural to ask whether there exists a permutation of that "destroys" all nontrivial 3-term arithmetic progressions (APs), in the sense tha…
Elliptic Curve Variants of the Least Quadratic Nonresidue Problem and Linnik's Theorem
Evan Chen, Peter S. Park, Ashvin Swaminathan
Let and be -nonisogenous, semistable elliptic curves over , having respective conductors and and both without com…
On Logarithmically Benford Sequences
Evan Chen, Peter S. Park, Ashvin Swaminathan
Let be an infinite subset, and let be a sequence of nonzero real numbers indexed by such that there exi…
Linnik's Theorem for Sato-Tate Laws on Elliptic Curves with Complex Multiplication
Evan Chen, Peter S. Park, Ashvin Swaminathan
Let be an elliptic curve with complex multiplication (CM), and for each prime of good reduction, let denote the trace of Fro…
On Arboreal Galois Representations of Rational Functions
Ashvin Swaminathan
The action of the absolute Galois group of a global field on a tree of iterated preimages of under …