From the 1 of 7 linked papers with an AI index.
7 papers
Beyond Mock Modularity: Elliptic Corrections for Higher Dyson Ranks
Claudia Alfes, Ken Ono, Ashvin Swaminathan
The paper investigates generating functions for higher Dyson ranks, revealing a hidden elliptic structure and providing explicit polynomial obstructions and correction terms that l…
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 partition theory. In 2010, the first author conjectured that, for every square-free $1<D\equiv 2…
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.,…