71 citations · 395 across the 32 of their papers we have counts for
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math.NT2009★ 2 cited
A note on the Mordell-Weil rank modulo n
Tim Dokchitser, Vladimir Dokchitser
Conjecturally, the parity of the Mordell-Weil rank of an elliptic curve over a number field K is determined by its root number. The root number is a product of local root numbers,…
math.NT2009★ 41 cited
Root numbers and parity of ranks of elliptic curves
Tim Dokchitser, Vladimir Dokchitser
The purpose of the paper is to complete several global and local results concerning parity of ranks of elliptic curves. Primarily, we show that the Shafarevich-Tate conjecture impl…