Arithmetic Dirichlet series and… to Theta series of lattices

• Arithmetic Dirichlet series and Tauberian methods
• Bounded Laplace and ordered Dirichlet boundary convergence
• The Chebotarev density theorem
• Class field theory
• Counting totally ramified extensions of a local field, and Serre's mass formula
• Diophantine approximation and transcendence
• Effective arithmetic bounds and geometry of numbers
• Global number fields, ray classes, adeles, and Hecke characters
• Global quadratic forms over number fields
• Heights, units and S-units of number fields
• Imaginary quadratic fields: class numbers, finiteness and class number one
• Integral quadratic forms and lattices
• Local fields and ramification
• Local Galois groups of p-adic fields
• Modular forms — Hecke theory, newforms, and L-functions
• Multiquadratic fields and genus theory
• Number fields, ramification, Frobenius, and the LMFDB invariants
• P-adic functional analysis
• Quadratic forms and cohomological invariants
• Theta series of lattices

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