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Inhomogeneous cubic congruences and rational points on del Pezzo surfaces
-
Stephan Baier
and
Tim D. Browning
Published/Copyright:
April 3, 2012
Abstract
For given non-zero integers a, b, q we investigate the density of solutions (x, y) ∈ ℤ2 to the binary cubic congruence ax2 + by3 ≡ 0 mod q, and use it to establish the Manin conjecture for a singular del Pezzo surface of degree 2 defined over ℚ.
Received: 2011-05-07
Revised: 2011-09-20
Published Online: 2012-04-03
Published in Print: 2013-06
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces
- On nonary cubic forms: IV
- Convexity estimates for level sets of quasiconcave solutions to fully nonlinear elliptic equations
- Inhomogeneous cubic congruences and rational points on del Pezzo surfaces
- A reduction theorem for the Alperin–McKay conjecture
- Regularity of solutions to the parabolic fractional obstacle problem
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