Analytic Number Theory by William Duke, Yuri Tschinkel

Book Contents :-
1. The Life and Work of Gustav Lejeune Dirichlet (1805–1859) 2. An Overview of Manin’s Conjecture for del Pezzo Surfaces 3. The Density of Integral Solutions for Pairs of Diagonal Cubic Equations 4. Second Moments of GL2 Automorphic L-Functions 5. CM Points and Weight 3/2 Modular Forms 6. The Path to Recent Progress on Small Gaps Between Primes 7. Negative Values of Truncations to L(1, ?) 8. Long Arithmetic Progressions of Primes 9. Heegner Points and Non-Vanishing of Rankin/Selberg L-Functions 10. Singular Moduli Generating Functions for Modular Curves and Surfaces 11. Rational Points of Bounded Height on Threefolds 12. Reciprocal Geodesics 13. The Fourth Moment of Dirichlet L-Functions 14. The Gauss Class-Number Problems

About this book :-
"Analytic Number Theory: A Tribute to Gauss and Dirichlet" by William Duke and Yuri Tschinkel provides a modern exploration of "number theory" through "analytic methods". The book introduces readers to key concepts such as "prime numbers", "L-functions", and "modular forms", blending classical results with contemporary research. It emphasizes both foundational ideas and recent breakthroughs, making complex topics accessible to advanced students and researchers alike. The text focuses on how "analytic techniques" can be applied to solve deep problems in number theory. It highlights the connections between classical approaches and modern tools, showing how rigorous proofs and examples illuminate the structure of integers and the distribution of primes. The authors also discuss open problems and current directions, offering insight into ongoing research in the field. Designed for graduate students, researchers, and anyone interested in the mathematics of numbers, "Analytic Number Theory" balances theoretical rigor with practical examples. It serves as both a reference and a learning resource, illustrating how analytic tools enrich the study of "number theory", enhance understanding of modular forms, and deepen knowledge of L-functions, primes, and related structures.

Book Detail :-
Title: Analytic Number Theory by William Duke, Yuri Tschinkel
Publisher: American Mathematical Society
Year: 2007
Pages: 266
Type: PDF
Language: English
ISBN-10 #: 0821843079
ISBN-13 #: 978-0821843079
License: External Educational Resource
Amazon: Amazon

About Author :-
The author William Duke and Yuri Tschinkel are leading "mathematicians" specializing in "number theory", "analytic number theory", and "arithmetic geometry". Duke, a professor at Duke University, is known for his work on "modular forms", "L-functions", and equidistribution, while Tschinkel, at NYU, focuses on "Diophantine geometry" and rational points. Together, they co-edited "Analytic Number Theory: A Tribute to Gauss and Dirichlet", showcasing cutting-edge research and developments in the field. The book highlights modern techniques, historical context, and key problems in "analytic number theory", offering insights for researchers, students, and anyone interested in the deep connections between numbers, geometry, and arithmetic.

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