Arithmetic Geometry, Number Theory, and Computation 1st Edition by Jennifer S. Balakrishnan 9783030809140 3030809145

Arithmetic Geometry, Number Theory, and Computation 1st Edition Jennifer S. Balakrishnan – Ebook Instant Download/Delivery ISBN(s): 9783030809133,3030809137, 9783030809140, 3030809145

Product details:

• ISBN 10: 3030809145
• ISBN 13: 9783030809140
• Author: Jennifer S. Balakrishnan

This volume contains articles related to the work of the Simons Collaboration “Arithmetic Geometry, Number Theory, and Computation.” The papers present mathematical results and algorithms necessary for the development of large-scale databases like the L-functions and Modular Forms Database (LMFDB). The authors aim to develop systematic tools for analyzing Diophantine properties of curves, surfaces, and abelian varieties over number fields and finite fields. The articles also explore examples important for future research.

Table contents:

A Robust Implementation for Solving the S-Unit Equation and Several Applications
Computing Classical Modular Forms for Arbitrary Congruence Subgroups
Square Root Time Coleman Integration on Superelliptic Curves
Computing Classical Modular Forms
Elliptic Curves with Good Reduction Outside of the First Six Primes
Efficient Computation of BSD Invariants in Genus 2
Restrictions on Weil Polynomials of Jacobians of Hyperelliptic Curves
Zen and the Art of Database Maintenance
Effective Obstruction to Lifting Tate Classes from Positive Characteristic
Conjecture: 100% of Elliptic Surfaces Over have Rank Zero
On Rational Bianchi Newforms and Abelian Surfaces with Quaternionic Multiplication
A Database of Hilbert Modular Forms
Isogeny Classes of Abelian Varieties over Finite Fields in the LMFDB
Computing Rational Points on Rank 0 Genus 3 Hyperelliptic Curves
Curves with Sharp Chabauty-Coleman Bound
Chabauty–Coleman Computations on Rank 1 Picard Curves
Linear Dependence Among Hecke Eigenvalues
Congruent Number Triangles with the Same Hypotenuse
Visualizing Modular Forms
A Prym Variety with Everywhere Good Reduction over
The S-Integral Points on the Projective Line Minus Three Points via Finite Cover

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