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On primes represented by aX^2+bY^3 - Jori Merikoski (Oxford)
2025-05-13 13:30 - 14:30 UTC | MR13
Let a,b > 0 be coprime integers. Assuming a conjecture on Hecke eigenvalues along binary cubic forms, we prove an asymptotic formula for the number of primes of the form ax^2 + by^3 with x ≤ X1/2 and y ≤ X1/3. The proof combines sieve methods with the theory of real quadratic fields/indefinite binary quadratic forms, the Weil bound for exponential sums, and spectral methods of GL(2) automorphic forms. We also discuss applications to elliptic curves.
