scholarly journals On $p$-Adic Zeta Functions and Class Groups of $\mathbb{Z}_{p}$-Extensions of certain Totally Real Fields

2018 ◽  
Author(s):  
Hisao Taya
Keyword(s):  
Zeta Functions ◽  
Class Groups ◽  
Totally Real ◽  
Totally Real Fields

scholarly journals Abelian surfaces over totally real fields are potentially modular

2021 ◽  
Author(s):  
George Boxer ◽  
Frank Calegari ◽  
Toby Gee ◽  
Vincent Pilloni
Keyword(s):  
Functional Equations ◽  
Zeta Functions ◽  
Meromorphic Continuation ◽  
Abelian Surfaces ◽  
Quadratic Extensions ◽  
Genus 2 ◽  
Genus One ◽  
Totally Real ◽  
Totally Real Fields

AbstractWe show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse–Weil zeta functions. We furthermore show the modularity of infinitely many abelian surfaces $A$ A over ${\mathbf {Q}}$ Q with $\operatorname{End}_{ {\mathbf {C}}}A={\mathbf {Z}}$ End C A = Z . We also deduce modularity and potential modularity results for genus one curves over (not necessarily CM) quadratic extensions of totally real fields.

scholarly journals Λ-adic modular symbols over totally real fields

2011 ◽  
pp. 841-865 ◽  
Author(s):  
Baskar Balasubramanyam ◽  
Matteo Longo
Keyword(s):  
Modular Symbols ◽  
Totally Real ◽  
Totally Real Fields

scholarly journals Motives over totally real fields and $p$-adic $L$-functions

1994 ◽  
Vol 44 (4) ◽  
pp. 989-1023 ◽  
Author(s):  
Alexei A. Panchishkin
Keyword(s):  
Totally Real ◽  
Totally Real Fields
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