Average Analytic Ranks of Elliptic Curves over Number Fields by Tristan Phillips

“…In particular, under the assumptions that all elliptic curves over a number field K are modular and have L-functions which satisfy the Generalized Riemann Hypothesis, we show that the average analytic rank of isomorphism classes of elliptic curves over K is bounded above by $(9\deg (K)+1)/2$ , when ordered by naive height. …”
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