On rank conjecture

Details On rank conjecture On rank conjecture

2011-04-04

arxiv.org/abs/1104.0609v4

Mathematics

Number Theory

11 pages; result is extended to all Q-curves

Scientific paper

The rank conjecture says that rank of elliptic curve with complex
multiplication is one less an arithmetic complexity of the corresponding
noncommutative torus with real multiplication. We prove the conjecture for the
so-called Q-curves introduced by B. H. Gross.

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