Very impressive. This is a great contribution from you to all students of algebraic geometry. Thank you very much. Bless your kind soul! Wish you all the best.

I wanted to know about approaches that were not already known to me. Besides some overly strict people are raising objection to the question itself as being subjective and argumentative, in the comments over there. I was in fear of the question getting closed and so steered away from anything with any hint of speculation. Note that by such fears I already CW-ed the question.

Nothing in the book of Ivic or Titchmarsch and Heath-Brown. More precisely, methods outside the traditional sybjects of elementary number theory and analytic number theory. I have given two examples above. One with algebraic geometry and one with thermodynamics.