Higher Math: Analytic Number Theory

References:

• Serre, Course in Arithmetic
• Sarnak notes: link.
• Tony Feng course notes: PDF.
• MO: How are holomorphic and real-analytic Eisenstein series related?
• Wiki

Riemann-Roch over arbitrary fields

See MO: Is there a Riemann-Roch for smooth projective curves over an arbitrary field? or a book on function fields, like Stichtenoth, Algebraic Function Fields and Codes.

Connection to Tate's thesis & Poisson summation

See any good reference on Tate's thesis. See e.g. MSE: Tate's Thesis: in what sense is Tate's Theorem 4.2.1 the Riemann-Roch theorem for curves? for an immediate online answer.