Arithmetic geometry, number theory, and computation

by Balakrishnan, Jennifer S. Elkies, Noam Hassett, Brendan Poonen, Bjorn Sutherland, Andrew V. Voight, John, (Mathematician)

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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 im…

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Title Statements

Full title :Arithmetic geometry, number theory, and computation / Jennifer S. Balakrishnan, Noam Elkies, Brendan Hassett, Bjorn Poonen, Andrew V. Sutherland, John Voight, editors.

Summary

Edition Statements

Publication Date:2021.

Publication Statements

Publisher(s):Springer
Place of Publication:Cham, Switzerland
Language:eng
Publication Date:2021.

The Physical Object

Description:1 online resource

Edition Identifiers

ISBN:9783030809140, 3030809145, 9783030809157, 3030809153, 9783030809164, 3030809161
DOI:10.1007/978-3-030-80914-0
oclc:on1304247904
LC Classification:QA242.5
Dewey Decimal:516.3/5

A robust implementation for solving the S-unit equation and several application (C. Rasmussen) -- Computing classical modular forms for arbitrary congruence subgroups (E. Assaf) -- Square root time Coleman integration on superelliptic curves (A. Best) -- Computing classical modular forms ( A. Sutherland) -- Elliptic curves with good reduction outside of the first six primes (B. Matschke) -- Efficient computation of BSD invariants in genus 2 (R. van Bommel) -- Restrictions on Weil polynomials of Jacobians of hyperelliptic curves (E. Costa) -- Zen and the art of database maintenance (D. Roe) -- Effective obstructions to lifting Tate classes from positive characteristic (E. Costa) -- Conjecture: 100% of elliptic surfaces over Q have rank zero (A. Cowan) -- On rational Bianchi newforms and abelian surfaces with quaternionic multiplication (J. Voight) -- A database of Hilbert modular forms (J. Voight) -- Isogeny classes of Abelian Varieties over Finite Fields in the LMFDB (D. Roe) -- Computing rational points on genus 3 hyperelliptic curves (S. Hashimoto) -- Curves with sharp Chabauty-Coleman bound (S. Gajovic) -- Chabauty-Coleman computations on rank 1 Picard curves (S. Hashimoto) -- …

Subjects

Arithmetical algebraic geometry Electronic Data Processing Géométrie algébrique Géométrie algébrique arithmétique Geometry, Algebraic Informatique Number theory Théorie des nombres