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On primes represented by aX^2+bY^3

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  • UserJori Merikoski (Oxford)
  • ClockTuesday 13 May 2025, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jef Laga .

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 ax2 + by3 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.

This talk is part of the Number Theory Seminar series.

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