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EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE

  • JOHANNES SPRANG (a1)

Abstract

A classical construction of Katz gives a purely algebraic construction of Eisenstein–Kronecker series using the Gauß–Manin connection on the universal elliptic curve. This approach gives a systematic way to study algebraic and $p$ -adic properties of real-analytic Eisenstein series. In the first part of this paper we provide an alternative algebraic construction of Eisenstein–Kronecker series via the Poincaré bundle. Building on this, we give in the second part a new conceptional construction of Katz’ two-variable $p$ -adic Eisenstein measure through $p$ -adic theta functions of the Poincaré bundle.

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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

References

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EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE

  • JOHANNES SPRANG (a1)

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