Conditional on GRH and modularity, the m-th moment of analytic rank of elliptic curves over a degree-d number field is bounded by O((9dm/2)^m), with a corresponding exponential tail bound.
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Upper bounds for moments of analytic ranks of elliptic curves over number fields
Conditional on GRH and modularity, the m-th moment of analytic rank of elliptic curves over a degree-d number field is bounded by O((9dm/2)^m), with a corresponding exponential tail bound.