179 citations · 1.4k across the 75 of their papers we have counts for
Showing 2005 · math.NTShow all
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math.NT2005★ 57 cited
Twists of X(7) and primitive solutions to x^2+y^3=z^7
Bjorn Poonen, Edward F. Schaefer, Michael Stoll
We find the primitive integer solutions to x^2+y^3=z^7. A nonabelian descent argument involving the simple group of order 168 reduces the problem to the determination of the set of…
math.NT2005★ 11 cited
Uniform first-order definitions in finitely generated fields
Bjorn Poonen
We prove that there is a first-order sentence in the language of rings that is true for all finitely generated fields of characteristic 0 and false for all fields of characteristic…
math.NT2005★ 1 cited
Heuristics for the Brauer-Manin obstruction for curves
Bjorn Poonen
We conjecture that if C is a curve of genus >1 over a number field k such that C(k) is empty, then a method of Scharaschkin (equivalent to the Brauer-Manin obstruction in the conte…