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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

7 votes
2 answers
1k views

What is the rational rank of the elliptic curve x^3 + y^3 = 2?

In Unsolved Problems in Number Theory, 3rd edition, section D1, 2004, R. K. Guy says, "Andrew Bremner has computed the rational rank of the elliptic curve x^3 + y^3 = Taxicab(n) as equal to 2, 4, 5, 4 …
Jonathan Sondow's user avatar
1 vote
0 answers
249 views

Is the rank of the elliptic curve x^3 + y^3 = a(n), where a(n) is the n-th cubefree taxicab ...

Is the rank of the elliptic curve x^3 + y^3 = a(n) over the rationals, where a(n) is the n-th cubefree taxicab number A080642(n) in the OEIS, known?
Jonathan Sondow's user avatar
21 votes
3 answers
6k views

Did André Weil predict that the Riemann Hypothesis would be settled by prime number theory r...

Did André Weil predict that the Riemann Hypothesis would be settled by prime number theory rather than by analysis? If so, what are a reference and/or a quotation?
Jonathan Sondow's user avatar