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Algebra Number Theory

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Algebra Number Theory

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Research Frontiers in Elliptic Curves and Rational Points

Investigation of rational point distribution on elliptic curves and connections to the Birch and Swinnerton-Dyer conjecture.

Arithmetic Dynamics on Elliptic Curve Families
Height Functions and Unlikely Intersection Problems
Rational Points via Descent and Obstruction Theory
Modularity and L-Function Zeros in Families
Torsion Point Distribution in Higher-Dimensional Jacobians
Effective Bounds on Mordell-Weil Rank Growth
Elliptic Curves over Function Fields and Specialization
Isogeny Graphs and Cryptographic Point Computation
Conductor Reduction and Singular Fiber Classification
Galois Representations from Cyclotomic Rational Points

All Algebra & Number Theory PhD categories