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Abstract analytic number theory
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211	MODULAR FORMS AND CALABI-YAU VARIETIES KAPIL PARANJAPE1 AND DINAKAR RAMAKRISHNAN2 Introduction Let f (z) = Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2014-04-02 03:40:44 Modular forms Analytic number theory Group theory Algebraic geometry Algebraic curves Elliptic curve Calabi–Yau manifold Motive Congruence subgroup Abstract algebra Mathematical analysis Mathematics
212	Galois Symbols on the square of an elliptic curve by Jacob Murre and Dinakar Ramakrishnan∗ Abstract We prove some theorems concerning the Galois symbol map Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2005-07-19 11:40:28 Field theory Galois theory Analytic number theory Elliptic curve Group theory Algebraic number field Field Semistable abelian variety Splitting of prime ideals in Galois extensions Abstract algebra Algebra Algebraic number theory
213	The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1 arXiv:1312.7859v1 [math.NT] 30 Dec[removed]Manjul Bhargava and Arul Shankar Add to Reading List Source URL: arxiv.org Language: English - Date: 2013-12-31 01:15:54 Number theory Elliptic curves Analytic number theory Group theory Modular forms Birch and Swinnerton-Dyer conjecture Curve J-invariant Tate–Shafarevich group Mathematics Abstract algebra Mathematical analysis
214	M ath. Res. Lett. c International Press[removed]), no. 2, 315–332 Add to Reading List Source URL: www.math.caltech.edu Language: English - Date: 2008-02-08 19:20:50 Automorphic forms Representation theory of Lie groups Conjectures Number theory Analytic number theory Cuspidal representation Multiplicity-one theorem Modular form Local Langlands conjectures Abstract algebra Mathematics Algebra
215	BIOGRAPHICAL DATA Dorian Goldfeld Personal Data U.S. Citizen, Birthdate: January 21, 1947, Marburg, Germany Married with two children. Add to Reading List Source URL: www.math.columbia.edu Language: English - Date: 2012-06-24 12:20:31 Analytic number theory Number theory Automorphic forms Number theorists Conjectures Kloosterman sum Eisenstein series Converse theorem Dorian M. Goldfeld Mathematics Mathematical analysis Abstract algebra
216	Elliptic Curves & Number Theory R. Sujatha School of Mathematics TIFR 1 Add to Reading List Source URL: www.ias.ac.in Language: English - Date: 2005-07-28 02:53:29 Analytic number theory Elliptic curve Group theory Number theory Pythagorean theorem Birch and Swinnerton-Dyer conjecture Congruent number Mathematics Abstract algebra Geometry
217	Statement of Research Interests Jay Daigle 1 Introduction Add to Reading List Source URL: jaydaigle.net Language: English - Date: 2014-06-04 22:53:47 Algebraic number theory Conjectures Diophantine geometry Field theory Analytic number theory Special values of L-functions Weil conjecture on Tamagawa numbers Algebraic number field Motive Abstract algebra Algebra Mathematics
218	JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 12, Number 1, January 1999, Pages 173–240 S[removed][removed]PERIODS OF AUTOMORPHIC FORMS Add to Reading List Source URL: www.math.columbia.edu Language: English - Date: 2007-02-16 14:25:12 Spectral theory Operator theory Analytic number theory Modular form Moduli theory Spectrum Algebraic number field Spectral theory of ordinary differential equations Plancherel theorem for spherical functions Abstract algebra Mathematical analysis Algebra
219	RANKS OF QUADRATIC TWISTS OF ELLIPTIC CURVES by Mark Watkins, Stephen Donnelly, Noam D. Elkies, Tom Fisher, Andrew Granville & Nicholas F. Rogers Abstract. — We report on a large-scale project to investigate the ranks Add to Reading List Source URL: magma.maths.usyd.edu.au Language: English - Date: 2014-09-26 14:36:32 Conjectures Analytic number theory Millennium Prize Problems Group theory Number theory Elliptic curve Birch and Swinnerton-Dyer conjecture Quadratic residue Curve Mathematics Abstract algebra Algebra
220	Analytic Number Theory Homework #4 (due Thursday, May 8, 2014) Problem 1: Let χ be a Dirichlet character (mod q) for some integer q > 1. Prove that L(1, χ) log q. Problem 2: Fix a prime p. Show that Add to Reading List Source URL: www.math.columbia.edu Language: English - Date: 2014-04-16 14:02:50 Number theory Analytic number theory Modular forms Moduli theory Dirichlet character Coprime Root of unity Modular curve Mathematics Abstract algebra Mathematical analysis