Arithmetic Geometry, Number Theory, and Computation
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Beschreibung
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.
Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
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.
Specific topics include● algebraic varieties over finite fields● the Chabauty-Coleman method● modular forms● rational points on curves of small genus● S-unit equations and integral points.
Presents number theory as a computational discipline Focuses on key examples central to future research Supports foundational work at the intersection of arithmetic geometry and data science
Autor*in
Jennifer S. Balakrishnan
Themen in »Arithmetic Geometry, Number Theory, and Computation«
elliptic curves subgroups zeta functions Hecke operators Birch-Swinnerton-Dyer conjecture Jacobians Hilbert modular forms Weil polynomials Galois groups hypersymmetric Abelian varieties Chabauty–Coleman method