Teoria Analítica dos Números

Pré-requesitos: Variável Complexa

Arithmetic functions; The Riemann zeta-function; Dirichlet characters; Dirichlet L-functions; Gauss sums; Ciclotomy; Primes in arithmetic progression; Functional equation for L-functions; Zero-free regions for z (s) and other L-functions; Prime Number Theorem; Siegel’s theorem; Sieve methods; Exponential sums; Consequences of the Riemann hypothesis; Explicit formulas; Extremal functions and Fourier analysis methods; Elliptic functions; Weierstrass P-function; Eisenstein series; Identities involving sums of powers of divisors; Ramanujan tau function; Jacobi theta functions; Two-squares theorem; Four-squares theorem.

[1] CHANDRASEKHARAN, K. – Elliptic functions, Springer, 1985.
[2] DAVENPORT, H. – Multiplicative Number Theory, Third Edition, Springer, 2000.
[3] IWANIEC, H., KOWALSKI, E. – Analytic Number Theory, AMS Colloquium Publications, Volume 53, 2004.
[4] STEIN, E. M., SHAKARCHI, R. – Complex analysis, Princeton Lectures in Analysis, II, Princeton University Press, 2003.
[5] TITCHMARSH, E. C., – The theory of the Riemann zeta-function, Second Edition, Oxford Science Publications, 1986.
[6] ZAGIER, D. – Elliptic modular forms and their applications, Universitext, Springer, 2008.