In number theory, the Stark conjectures, introduced by Stark (1971, 1975, 1976, 1980) and later expanded by Tate (1984), give conjectural information about the coefficient of the leading term in the Taylor expansion of an Artin L-function associated with a Galois extension K/k of algebraic number fields. The conjectures generalize the analytic class number formula expressing the leading coefficient of the Taylor series for the Dedekind zeta function of a number field as the product of a regulator related to S-units of the field and a rational number.
When K/k is an abelian extension and the order of vanishing of the L-function at s = 0 is one, Stark gave a refinement of his conjecture, predicting the existence of certain S-units, called Stark units, which generate abelian extensions of number fields.
In number theory, the Starkconjectures, introduced by Stark (1971, 1975, 1976, 1980) and later expanded by Tate (1984), give conjectural information about...
correcting and completing the earlier work of Kurt Heegner, and for Stark'sconjecture. More recently, he collaborated with Audrey Terras to study zeta functions...
This is a list of notable mathematical conjectures. The following conjectures remain open. The (incomplete) column "cites" lists the number of results...
subgroups are at least 1 / 4 {\displaystyle 1/4} . Stark conjectures (including Brumer–Starkconjecture) Characterize all algebraic number fields that have...
main conjecture of Iwasawa theory in the totally real μ = 0 case. Together with Samit Dasgupta and Kevin Ventullo, he proved the Gross–Starkconjecture. In...
Gras conjectures and Rubin's integral refinement of the abelian Starkconjectures. He has also made important contributions to the Starkconjectures over...
stating the first two conjectures, and discusses real quadratic fields in Article 304, stating the third conjecture. Gauss conjecture (class number tends...
1944) is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel...
{\displaystyle c} . A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. Mathematician...
number fields. In particular, Dasgupta's research has focused on the Starkconjectures and Heegner points. In 2009, Dasgupta received a Sloan Research Fellowship...
physicist Judith Young. CEILIDH Torus-based cryptography Euler system Starkconjectures Rubin, Karl (1989). "Tate-Shafarevich groups of elliptic curves with...
the OEIS) This result was conjectured by Gauss and proved up to minor flaws by Kurt Heegner in 1952. Alan Baker and Harold Stark independently proved the...
by Armand Brumer Brumer–Starkconjecture, a conjecture in algebraic number theory, named after Armand Brumer and Harold Stark Brumer Islands, an island...
imaginary quadratic extension of a totally real field. In 1974, Harold Starkconjectured that there are finitely many CM fields of class number 1. He showed...
equivariant Tamagawa number conjecture: a survey", in Burns, David; Popescu, Christian; Sands, Jonathan; et al. (eds.), Stark'sconjectures: recent work and new...
these ideas are further combined with Stickelberger's theorem. Brumer–Starkconjecture Smith–Minkowski–Siegel mass formula Lectures on the Dirichlet class...
setting. This led Weil (1949) to conjecture a similar statement for all algebraic varieties; the resulting Weil conjectures were proved by Pierre Deligne (1974...
further identities relating these functions, equivalent to the mock theta conjectures, that were proved by Hickerson. Andrews found representations of many...
2013-03-08 at the Wayback Machine. Closed Orbit Bifurcations in Continuum Stark Spectra, M Courtney, H Jiao, N Spellmeyer, D Kleppner, J Gao, JB Delos,...
appreciation by the people of the Shire, gets "defeat and disillusionment—the stark, bitter ending typical of the Iliad, Beowulf, the Morte D'Arthur". In other...
Theater in Detroit, Michigan. These were the basis for the concert film Stark Raving Black, which appeared in theaters for a limited time in October,...
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