Titlebook: Arithmetic Geometry, Number Theory, and Computation; Jennifer S. Balakrishnan,Noam Elkies,John Voight Conference proceedings 2021 The Edit

Friction

Conference proceedings 2021t 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 fin

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A Robust Implementation for Solving the ,-Unit Equation and Several Applications,n . + . = 1, . in the computer algebra package SageMath. This paper outlines the mathematical basis for the implementation. We discuss and reference the results of extensive computations, including exponent bounds for solutions in many fields of small degree for small sets .. As an application, we p

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rectocele

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Efficient Computation of BSD Invariants in Genus 2,ns and Modular Forms Database [.]. This report explains the improvements made to the implementation of the algorithm described in [.] that were needed to do the computation of the Tamagawa numbers and the real period in reasonable time. We also explain some of the more technical details of the algor

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Ophthalmologist

Zen and the Art of Database Maintenance,ining a mathematical database. In particular, we report on the transition of the . (LMFDB) between two database systems. We also highlight some of the improvements to the LMFDB that we have made as part of this transition.

MIRE

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lethargy

On Rational Bianchi Newforms and Abelian Surfaces with Quaternionic Multiplication, curves, but instead to abelian surfaces with quaternionic multiplication. Two of these examples exhibit a rather special kind of behaviour: we show they arise from twisted base change of a classical newform with nebentypus character of order 4 and eight inner twists.