In *"On the history of the Weil Conjectures"* Dieudonné says:
*"Appropriately enough, the story, as with so many problems in number theory, begins with Gauss..."*.

C. F. Gauss, Disquisitiones Arithmeticae; Mathematisches Tagebuch.

A letter to Gauss(1827), C. G. Jacobi.

V. A. Lebesgue work on this type of equations(1837).

Hardy and Littlewood work on the singular series for Waring's problem.

I know that: Hasse proved a conjecture due to Artin about the "Riemann Hypothesis" for curves of genus 1 over Finite fields, Artin conjectured the zeroes of a rational function with coefficients in Q would all be on the circle [u]=q^1/2, and verified that conjecture for many polynomials P of low degree, Weil proved the "Riemann Hypothesis" for a curve of arbitrary genus and for some kind of hypersurfaces and grassmannians among other types of varieties.

My questions are:

What happened between Hardy and Weil work?

Which are the papers of this works?

Is there any book that contains these works?