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Algebraic varieties. --- Rational points (Geometry). --- Rational points (Geometry) --- Algebraic varieties --- Points, Rational (Geometry) --- Varieties, Algebraic --- Arithmetical algebraic geometry --- Geometry, Algebraic --- Linear algebraic groups --- Number theory --- Algebraic geometry
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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 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.
Number theory --- Geometry --- Computer science --- landmeetkunde --- toegepaste informatica --- computers --- getallenleer --- computerkunde
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Number theory --- Geometry --- Computer science --- landmeetkunde --- toegepaste informatica --- computers --- getallenleer --- computerkunde --- Number theory. --- Number study --- Numbers, Theory of --- Algebra --- Geometria algebraica aritmètica --- Teoria de nombres --- Teoria dels nombres --- Àlgebra --- Anàlisi diofàntica --- Arrels de la unitat --- Congruències i residus --- Conjectura de Catalan --- Darrer teorema de Fermat --- Formes automorfes --- Formes quadràtiques --- Fórmula de traça de Selberg --- Funcions aritmètiques --- Funcions L --- Funcions modulars --- Funcions recursives --- Funcions zeta --- Geometria de nombres --- Grups modulars --- Lleis de reciprocitat --- Nombres de Fermat --- Nombres ordinals --- Nombres p-àdics --- Nombres transfinits --- Numeració --- Particions (Matemàtica) --- Quadrats màgics --- Sedàs (Matemàtica) --- Teorema de Fermat --- Teorema de Gödel --- Teoria algebraica de nombres --- Teoria de Galois --- Cossos algebraics --- Geometria algèbrica aritmètica --- Geometria diofàntica --- Geometria algebraica --- Punts racionals (Geometria) --- Varietats de Shimura
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