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Arithmetic Geometry, Number Theory, and Computation /

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...

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Bibliographic Details
Corporate Author: SpringerLink (Online service)
Other Authors: Balakrishnan, Jennifer S. (Editor), Elkies, Noam (Editor), Hassett, Brendan (Editor), Poonen, Bjorn (Editor), Sutherland, Andrew V. (Editor), Voight, John (Editor)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2021.
Edition:1st ed. 2021.
Series:Simons Symposia,
Subjects:
Algebraic geometry.
Number theory.
Computer science.
Algebraic Geometry.
Number Theory.
Theory of Computation.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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. Gajović)
  • Chabauty-Coleman computations on rank 1 Picard curves (S. Hashimoto)
  • Linear dependence among Hecke eigenvalues (D. Kim)
  • Congruent number triangles with the same hypotenuse (D. Lowry-Duda)
  • Visualizing modular forms (D. Lowry-Duda)
  • A Prym variety with everywhere good reduction over Q(√ 61) ( J. Voight)
  • The S-integral points on the projective line minus three points via étale covers and Skolem's method (B. Poonen).