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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