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The four papers collected in this book discuss advanced results in analytic number theory, including recent achievements of sieve theory leading to asymptotic formulae for the number of primes represented by suitable polynomials; counting integer solutions to Diophantine equations, using results from algebraic geometry and the geometry of numbers; the theory of Siegels zeros and of exceptional characters of Lfunctions; and an uptodate survey of the axiomatic theory of Lfunctions introduced by Selberg.
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