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.

About the Author

Jennifer Balakrishnan is Clare Boothe Luce Associate Professor of Mathematics and Statistics at Boston University. She holds a Ph.D. in Mathematics from the Massachusetts Institute of Technology.

Noam Elkies is Professor of Mathematics at Harvard University. He holds a Ph.D. in Mathematics from Harvard University.

Brendan Hassett is Professor of Mathematics at Brown University and Director of the Institute for Computational and Experimental Research in Mathematics. He holds a Ph.D. in Mathematics from Harvard University.

Bjorn Poonen is Distinguished Professor in Science at the Massachusetts Institute of Technology. He holds a Ph.D. in Mathematics from the University of California at Berkeley.

Andrew Sutherland is Principal Research Scientist at the Massachusetts Institute of Technology. He holds a Ph.D. in Mathematics from the Massachusetts Institute of Technology.

John Voight is Professor of Mathematics at Dartmouth College. He holds a Ph.D. in Mathematics from the University of California at Berkeley.

"About this title" may belong to another edition of this title.

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