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Molina Blanco, Santiago;
Extremal p-Adic L-Functions
In this note, we propose a new construction of cyclotomic p-adic L-functions that are attached to classical modular cuspidal eigenforms. This allows for us to cover most known cases to date and provides a method which is amenable to generalizations to automorphic forms on arbitrary groups. In the classical setting of GL2 over Q, this allows for us to construct the p-adic L-function in the so far uncovered extremal case, which arises under the unlikely hypothesis that p-th Hecke polynomial has a double root. Although Tate’s conjecture implies that this case should never take place for GL2/Q, the obvious generalization does exist in nature for Hilbert cusp forms over totally real number fields of even degree, and this article proposes a method that should adapt to this setting. We further study the admissibility and the interpolation properties of these extremal p-adic L-functionsLpext(f,s), and relate Lpext(f,s) to the two-variable p-adic L-function interpolating cyclotomic p-adic L-functions along a Coleman family.
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Differential equations, :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC], <i>p</i>-adic L-functions, :Matemàtiques i estadística::Equacions diferencials i integrals [Àrees temàtiques de la UPC], Equacions diferencials funcionals, p-adic L-functions, QA1-939, FOS: Mathematics, Number Theory (math.NT), Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals, :35 Partial differential equations::35C Representations of solutions [Classificació AMS], Extremal p-adic L-functions, Mathematics - Number Theory, Equacions en derivades parcials, Classificació AMS::35 Partial differential equations::35C Representations of solutions, Modular forms, Coleman families, Differential equations, Partial, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials, Classificació AMS::34 Ordinary differential equations::34M Differential equations in the complex domain, Mathematics, Partial, :34 Ordinary differential equations::34M Differential equations in the complex domain [Classificació AMS]
Differential equations, :Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials [Àrees temàtiques de la UPC], <i>p</i>-adic L-functions, :Matemàtiques i estadística::Equacions diferencials i integrals [Àrees temàtiques de la UPC], Equacions diferencials funcionals, p-adic L-functions, QA1-939, FOS: Mathematics, Number Theory (math.NT), Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals, :35 Partial differential equations::35C Representations of solutions [Classificació AMS], Extremal p-adic L-functions, Mathematics - Number Theory, Equacions en derivades parcials, Classificació AMS::35 Partial differential equations::35C Representations of solutions, Modular forms, Coleman families, Differential equations, Partial, Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials, Classificació AMS::34 Ordinary differential equations::34M Differential equations in the complex domain, Mathematics, Partial, :34 Ordinary differential equations::34M Differential equations in the complex domain [Classificació AMS]
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