The arithmetic of algebraic curves

Isabella Bashmakova

Type: Book-Chapter

Publication Date: 2019-01-18

Citations: 57

DOI: https://doi.org/10.1090/dol/054/12

Abstract

Equations over Finite Fields. Distribution of Quadratic Residues and Nonresidues. Historical Commentaries on Chapters 1 and 2. Rational Points on Algebraic Curves. The Riemann-Roch Theorem. The Riemann Hypothesis for Congruence Zetafunctions. Integral Points on Curves and Nonstandard Arithmetic. The Siegel-Mahler Theorem. Appendix: Hilbert's Tenth Problem. Index.

Locations

eScholarship (California Digital Library) - View - PDF
American Mathematical Society eBooks - View

Similar Works

Action	Title	Year	Authors
+	Arithmetic Algebraic Geometry	1991	Gerard van der Geer Frans J. Oort J. H. M. Steenbrink
+	Algebraic Curves over Finite Fields	1991	Carlos Moreno
+ PDF Chat	Arithmetic Algebraic Geometry	2008	Brian Conrad Karl Rubin
+	Elliptic curves: function theory, geometry, arithmetic	1998	H. P. McKean Victor H. Moll
+	Analytical principles of the theory of curves	1960	H. F. Baker
+	Algebraic Curves and Riemann Surfaces	1995	Rick Miranda
+	The Number Theory of Algebraic Curves	2007	Anthony W. Knapp
+	Algebraic Geometry	2022	Lubjana Beshaj
+	Elliptic Curves	1997	H. P. McKean Victor H. Moll
+	Algebraic Curves	2009	Joseph H. Silverman
+	Algebraic geometry and arithmetic curves	2003	Qing Liu
+	The Riemann-Roch theorem for algebraic curves	1963	Arthur Mattuck A. L. Mayer
+	The Riemann-Roch theorem for algebraic curves	1965	Paulo Ribenboim
+	Topics in the Theory of Algebraic Function Fields	2006	Villa Salvador Gabriel Daniel
+ PDF Chat	Elementary algebraic geometry	2017	Richard Evan Schwartz
+	Arithmetic geometry : computation and applications : 16th International Conference, Arithmetic, Geometry, Cryptography, and Coding Theory, June 19-23, 2017, Centre International de Rencontres Mathématiques, Marseille, France	2019	Yves Aubry Everett W. Howe Christophe Ritzenthaler
+ PDF Chat	The Arithmetic of Elliptic Curves	2020
+	The arithmetic of elliptic curves	1974	John Tate
+	Algebraic Geometry: An Introduction	2007	Daniel Perrin Catriona Maclean
+ PDF Chat	The arithmetic of quadratic forms	2006	五郎志村

Works That Cite This (53)

Action	Title	Year	Authors
+ PDF Chat	Sums of multiplicative characters with additive convolutions	2017	Aleksei Volostnov Ilya D. Shkredov
+	Optimal bounds for Büchi's problem in modular arithmetic	2014	Pablo Sáez Xavier Vidaux Maxim Vsemirnov
+	On curves covered by the Hermitian curve, II	1998	Antonio Cossidente Gábor Korchmáros Fernando Torres
+ PDF Chat	Codes on Superelliptic Curves	1998	Ferruh Özbudak Михаил Михайлович Глухов
+ PDF Chat	The Frequency of Elliptic Curve Groups over Prime Finite Fields	2015	Vorrapan Chandee Chantal David Dimitris Koukoulopoulos Ethan Smith
+ PDF Chat	Exponential Sums and Flowers	2022	N. V. Proskurin
+ PDF Chat	On Some Cubic Exponential Sums	2022	N. V. Proskurin
+ PDF Chat	On the diophantine equation $x^p-x=y^q-y$	1999	Max Mignotte A. Pethő
+	On Curves Covered by the Hermitian Curve	1999	Antonio Cossidente Gábor Korchmáros Fernando Torres
+	Artin–Schreier L-functions and random unitary matrices	2014	Alexei Entin

Works Cited by This (1)

Action	Title	Year	Authors
+	Fundamentals of Diophantine Geometry	1983	Serge Lang