Downloads provided by UsageCountsOn the Elliptic Stark Conjecture in higher weight
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Francesca Gatti; Xavier Guitart;
On the Elliptic Stark Conjecture in higher weight
We study the special values of the triple product $p$-adic $L$-function constructed by Darmon and Rotger at all classical points outside the region of interpolation. We propose conjectural formulas for these values that can be seen as extending the Elliptic Stark Conjecture, and we provide theoretical evidence for them by proving some particular cases.
Corrected some typographical errors and some references
11G40, 14G10, Teoria de nombres, Triple product p-adic l-functions, Zeta functions, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), triple product \(p\)-adic \(L\)-functions, Diophantine geometry, L-functions, Number theory, elliptic Stark conjecture, FOS: Mathematics, 14G05, Rational points, Funcions L, Number Theory (math.NT), :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Elliptic Stark Conjecture, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, triple product $p$-adic $L$-functions, Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry, Elliptic stark conjecture, Mathematics - Number Theory, modular forms, Funcions zeta, triple product p-adic L-functions, :Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC], Rational points (Geometry, :14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry [Classificació AMS], Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Geometria algèbrica--Aritmètica, Punts racionals (Geometria), Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], Aritmètica, Modularforms, Arithmetical algebraic geometry, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
11G40, 14G10, Teoria de nombres, Triple product p-adic l-functions, Zeta functions, Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry), triple product \(p\)-adic \(L\)-functions, Diophantine geometry, L-functions, Number theory, elliptic Stark conjecture, FOS: Mathematics, 14G05, Rational points, Funcions L, Number Theory (math.NT), :Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC], Elliptic Stark Conjecture, \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture, triple product $p$-adic $L$-functions, Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry, Elliptic stark conjecture, Mathematics - Number Theory, modular forms, Funcions zeta, triple product p-adic L-functions, :Matemàtiques i estadística::Àlgebra [Àrees temàtiques de la UPC], Rational points (Geometry, :14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry [Classificació AMS], Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Geometria algèbrica--Aritmètica, Punts racionals (Geometria), Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra, :11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) [Classificació AMS], Aritmètica, Modularforms, Arithmetical algebraic geometry, Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
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