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11
votes
1
answer
485
views
Siegel--Walfisz for number fields
For a number field $K$, we write $\Delta_K$ for its absolute discriminant. I was hoping for a Siegel--Walfisz type theorem of the following type:
Let $A > 0$. Then for every $X > 0$, every number fiel …
8
votes
0
answers
202
views
Elliptic curves of rank 1 over number fields
I am interested what is known about the following statement:
For every number field $K$, there exists an elliptic curve $E$ defined over $K$ with algebraic rank equal to $1$.
Is this statement known t …