Geodesic
EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE
Forum of Mathematics, Sigma, Tome 7 (2019)

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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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     author = {JOHANNES SPRANG},
     title = {EISENSTEIN{\textendash}KRONECKER {SERIES} {VIA} {THE} {POINCAR\'E} {BUNDLE}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
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     year = {2019},
     doi = {10.1017/fms.2019.29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.29/}
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JOHANNES SPRANG. EISENSTEIN–KRONECKER SERIES VIA THE POINCARÉ BUNDLE. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.29

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