Analytic Number Theory: A Tribute to Gauss and Dirichlet
American Mathematical Soc., 2007 - 256 pàgines
Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Gottingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet. Among the topics are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of $L$-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables.
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algebraic apply argument arithmetic progressions automorphic Berlin binary quadratic forms character class number class-number closed geodesics CM points consider constant corresponding cubic surface cusp forms defined del Pezzo surfaces denote discriminant Eisenstein series equation equidistributed estimate finite fixed follows form of weight Fourier coefficients Fourier expansion fundamental discriminant Gaufi Gauss geometrically integral Gottingen Heath-Brown Heegner points Hensel Hilbert modular surfaces Humboldt hyperplane Jacobi L-functions lectures Lejeune Dirichlet Lemma linear lower bound Maass forms Manin conjecture Math Mathematics Mathematics Subject Classification meromorphic method modular curve modular form multiplicative nonvanishing Note obtain paper Pezzo surfaces polynomial positive integer prime number primitive problem proof of Theorem Proposition prove rational points reciprocal result Riemann singular moduli solution Steiner surface subgroup subset suppose surfaces of degree Theorem 1.1 theta torsor traces of singular Tschinkel universal torsor upper bound values Zagier zeros zeta functions