Algebraic theta functions and the \(p\)-adic interpolation of Eisenstein-Kronecker numbers

DOI10.1215/00127094-2010-024zbMath1205.11076arXivmath/0610163OpenAlexW1998414450MaRDI QIDQ982686

Kenichi Bannai, Shin-ichi Kobayashi

Publication date: 7 July 2010

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610163

zbMATH Keywords

elliptic curvesabelian varietiestheta functionsp-adic measuressupersingularityHecke L-functionsp-adic L-functionsEisenstein-Kronecker numbers

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Complex multiplication and abelian varieties (14K22) Algebraic theory of abelian varieties (14K05)

Related Items (14)

p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas ⋮ Integral structures on \(p\)-adic Fourier theory ⋮ The radius of convergence of the \(p\)-adic sigma function ⋮ Periods of Hilbert modular forms, Kronecker series and cohomology ⋮ \(p\)-adic Eisenstein-Kronecker series and non-critical values of \(p\)-adic Hecke \(L\)-function of an imaginary quadratic field when the conductor is divisible by \(p\) ⋮ On arithmetic monodromy representations of Eisenstein type in fundamental groups of once punctured elliptic curves ⋮ \(A_{\infty}\)-algebras associated with elliptic curves and Eisenstein-Kronecker series ⋮ Canonical equivariant cohomology classes generating zeta values of totally real fields ⋮ The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes ⋮ Explicit \(t\)-expansions for the elliptic curve \(y^{2}= 4(x^{3}+Ax+B)\) ⋮ A higher-order generalization of Jacobi's derivative formula and its algebraic geometric analogue ⋮ Arithmetical Power Series Expansion of the Sigma Function for a Plane Curve ⋮ The syntomic realization of the elliptic polylogarithm via the Poincaré bundle ⋮ EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE

Cites Work

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