modularity theoremの例文

• Conrad and others proved the modularity theorem, also known as the Taniyama-Shimura Conjecture.
• This would conflict with the modularity theorem, which asserted that all elliptic curves are modular.
• Several theorems in number theory similar to Fermat's Last Theorem follow from the modularity theorem.
• For elliptic curves over the rational numbers, the Hasse Weil conjecture follows from the modularity theorem.
• In 1984, Gerhard Frey noticed an apparent link between the modularity theorem and Fermat's Last Theorem.
• In 1984, Gerhard Frey noted a link between Fermat's equation and the modularity theorem, then still a conjecture.
• This showed that a proof of the Serre's conjecture on modular Galois representations, which would imply the modularity theorem.
• Hearing of the 1986 proof of the epsilon conjecture, Wiles decided to begin working exclusively towards a proof of the modularity theorem.
• The modularity theorem, also known as the Taniyama Shimura conjecture, asserts that every elliptic curve defined over the rational numbers is modular.
• Several other theorems in number theory similar to Fermat's Last Theorem also follow from the same reasoning, using the modularity theorem.
• The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century.
• The remaining parts of the modularity theorem were subsequently proved by other mathematicians, building on Wiles's work, between 1996 and 2001 ..
• As such, a proof or disproof of either of Fermat's Last Theorem or the modularity theorem would simultaneously prove or disprove the other.
• It was subsequently shown to be true for all elliptic curves over "'Q "', as a consequence of the modularity theorem.
• These papers established the modularity theorem for semistable elliptic curves, the last step in proving Fermat's Last Theorem, 358 years after it was conjectured.
• "' Fred Irvin Diamond "'( born November 19, 1964 ) is a mathematician, known for his role in proving the modularity theorem for elliptic curves.
• In the 1950s and 1960s the modularity theorem, a connection between elliptic curves and modular forms, was conjectured by the Japanese mathematician Goro Shimura based on ideas posed by Yutaka Taniyama.
• The resulting modularity theorem ( at the time known as the Taniyama Shimura conjecture ) states that every elliptic curve is modular, meaning that it can be associated with a unique modular form.
• The modularity theorem implies a closely related analytic statement : to an elliptic curve " E " over "'Q "'we may attach a corresponding L-series.
• I've considered the spirit of WP : ACADEMIC . While the modularity theorem is a major theorem, I don't think Diamond has been notable because of his involvement in it.