Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
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The 'large sieve', an important technical tool of analytic number theory, has advanced extensively in recent years. This book develops a general form of sieve inequality, and describes its varied, sometimes surprising applications, with potential uses in fields as wide ranging as topology, probability, arithmetic geometry and discrete group theory.
About the Author
Emmanuel Kowalski is Professor in the Departement Mathematik at ETH Zürich.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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sieve setting, dual sieve, classical large sieve, probabilistic sieves, small splitting field, sieving sets, geometric monodromy group, elliptic divisibility sequences, sieve inequality, infinite abelianization, finite symmetric generating set, geometric conjugacy classes, implied constant depending, sieve support, group sieve, sieve bound, sieve constants, absolute implied, sifted set, irreducible linear representations, implied constant depends, linear disjointness, split torus, squarefree numbers, monodromy groups Key Phrases - Capitalized Phrases (CAPs): (learn more)
Gallagher's Theorem, Riemann Hypothesis, Groups of Lie, Virtual Haken Conjecture, Central Limit Theorem, Chinese Remainder Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
sieve setting, dual sieve, classical large sieve, probabilistic sieves, small splitting field, sieving sets, geometric monodromy group, elliptic divisibility sequences, sieve inequality, infinite abelianization, finite symmetric generating set, geometric conjugacy classes, implied constant depending, sieve support, group sieve, sieve bound, sieve constants, absolute implied, sifted set, irreducible linear representations, implied constant depends, linear disjointness, split torus, squarefree numbers, monodromy groups Key Phrases - Capitalized Phrases (CAPs): (learn more)
Gallagher's Theorem, Riemann Hypothesis, Groups of Lie, Virtual Haken Conjecture, Central Limit Theorem, Chinese Remainder Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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