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Analytic Number Theory
Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 11-18, 2002
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The four contributions collected in this volume deal with several advanced results in analytic number theory. Friedlander s paper contains some recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials. Heath-Brown's lecture notes mainly deal with counting integer solutions to Diophantine equations, using among other tools several results from algebraic geometry and from the geometry of numbers. Iwaniec s paper gives a broad picture of the theory of Siegel s zeros and of exceptional characters of L-functions, and gives a new proof of Linnik s theorem on the least prime in an arithmetic progression. Kaczorowski s article presents an up-to-date survey of the axiomatic theory of L-functions introduced by Selberg, with a detailed exposition of several recent results.
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