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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Computationally bounding a curve's genus from below?
It's a plane curve, and even though the degree is large it shouldn't be too hard to compute its Newton Polygon, and then it's (reasonably) easy to compute the geometric genus... Well, depending on ho …