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(参考)
https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture
Birch and Swinnerton-Dyer conjecture

Current status
The Birch and Swinnerton-Dyer conjecture has been proved only in special cases:

2.Gross & Zagier (1986) showed that if a modular elliptic curve has a first-order zero at s = 1 then it has a rational point of infinite order; see Gross–Zagier theorem.

3.Kolyvagin (1989) showed that a modular elliptic curve E for which L(E, 1) is not zero has rank 0, and a modular elliptic curve E for which L(E, 1) has a first-order zero at s = 1 has rank 1.

References
Gross, Benedict H.; Zagier, Don B. (1986). "Heegner points and derivatives of L-series". Inventiones Mathematicae. 84 (2): 225–320. Bibcode:1986InMat..84..225G. doi:10.1007/BF01388809. MR 0833192. S2CID 125716869.

https://en.wikipedia.org/wiki/Benedict_Gross
Benedict Hyman Gross is an American mathematician who is a professor at the University of California San Diego,[1] the George Vasmer Leverett Professor of Mathematics Emeritus at Harvard University, and former Dean of Harvard College.[2]

He is known for his work in number theory, particularly the Gross–Zagier theorem on L-functions of elliptic curves, which he researched with Don Zagier.

Education and Professional career
Gross graduated from The Pingry School, a leading independent school in New Jersey, in 1967 as the valedictorian. In 1971, he graduated Phi Beta Kappa from Harvard University. He then received an M.Sc. from Oxford University as a Marshall Scholar in 1974 before returning to Harvard and completing his Ph.D. in 1978, under John Tate.[2][3]