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7 papers · 1 filter
Local data of elliptic curves under quadratic twist
Alexander J. Barrios, Manami Roy, Nandita Sahajpal +3
Let be the field of fractions of a complete discrete valuation ring with a perfect residue field. In this article, we investigate how the Tamagawa number of changes under…
Explicit classification of isogeny graphs of rational elliptic curves
Alexander J. Barrios
Let be an integer such that has genus , and let be a field of characteristic or relatively prime to . In this article, we explicitly…
Representations attached to elliptic curves with a non-trivial odd torsion point
Alexander J. Barrios, Manami Roy
We give a classification of the cuspidal automorphic representations attached to rational elliptic curves with a non-trivial torsion point of odd order. Such elliptic curves are pa…
Lower bounds for the modified Szpiro ratio
Alexander J. Barrios
Let be an elliptic curve. The modified Szpiro ratio of is the quantity …
Local data of rational elliptic curves with non-trivial torsion
Alexander J. Barrios, Manami Roy
By Mazur's Torsion Theorem, there are fourteen possibilities for the non-trivial torsion subgroup of a rational elliptic curve. For each , such that may have additive re…
Global Automorphic Sobolev Theory and The Automorphic Heat Kernel
Amy T. DeCelles
Heat kernels arise in a variety of contexts including probability, geometry, and functional analysis; the automorphic heat kernel is particularly important in number theory and str…