Deninger's conjecture onL-functions of elliptic curves ats=3
Copyright policy )Deninger's conjecture onL-functions of elliptic curves ats=3
I compute explicitly the regulator map on $K_4(X)$ for an arbitrary curve $X$ over a number field. Using this and Beilinson's theorem about regulators for modular curves ([B2]) I prove a formula expressing the value of the $L$-function $L(E,s)$ of a modular elliptic curve $E$ over $\Bbb Q$ at $s=3$ by the double Eisenstein-Kronecker series.
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- Massachusetts Institute of Technology United States
\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Eisenstein-Kronecker series, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Mathematics - Algebraic Geometry, regulator map, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), special values of \(L\)-functions, Deninger's conjecture, FOS: Mathematics, modular elliptic curve, Algebraic Geometry (math.AG)
\(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, Eisenstein-Kronecker series, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Mathematics - Algebraic Geometry, regulator map, Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects), special values of \(L\)-functions, Deninger's conjecture, FOS: Mathematics, modular elliptic curve, Algebraic Geometry (math.AG)
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