Analytic Number Theory [electronic resource] : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 1118, 2002 / by J. B. Friedlander, D. R. Heath-Brown, H. Iwaniec, J. Kaczorowski ; edited by Alberto Perelli, Carlo Viola.

Producing Prime Numbers via Sieve Methods -- Counting Rational Points on Algebraic Varieties -- Conversations on the Exceptional Character -- Axiomatic Theory of L-Functions: the Selberg Class.

The four contributions collected in this volume deal with several advanced results in analytic number theory. Friedlanders 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. Iwaniecs paper gives a broad picture of the theory of Siegels zeros and of exceptional characters of L-functions, and gives a new proof of Linniks theorem on the least prime in an arithmetic progression. Kaczorowskis 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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