Mathematical Developments Arising from Hilbert Problems, Part 2

3-space abelian algebraic number field algebraic variety algorithm Amer analytic arbitrary arithmetic Artin automorphisms Beltrami boundary value bounded Calculus of Variations classical coefficients cohomology compact complex computable conformal mapping conics conjecture consider curve degree denote dimension Diophantine definition Diophantine equation Diophantine set domain elliptic equations enumerative equivalent example existence extension fact finite number formula Fuchsian group genus geometry given group G Hence Hilbert's tenth problem holomorphic inequality integers intersection isomorphism Kleinian group lattice linear manifold Math Mathematical method minimal surface Möbius transformation multiplicative natural numbers number theory obtained parameters partial differential equations polynomial positive definite prime proof proved Pure Appl quadratic forms quotient reciprocity law regular singular points relation representation result Riemann surface ring satisfying Schubert cycles Schubert variety solution solvable space subgroup subset tangent test function theorem tions topological variables variational problem vector Zariski