-adic -functions for modular forms
Shai Haran (1987)
Compositio Mathematica
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Shai Haran (1987)
Compositio Mathematica
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Alexei A. Panchishkin (1994)
Annales de l'institut Fourier
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Special values of certain functions of the type are studied where is a motive over a totally real field with coefficients in another field , and is an Euler product running through maximal ideals of the maximal order of and being a polynomial with coefficients in . Using the Newton and the Hodge polygons of one formulate a conjectural criterium for the existence of a -adic analytic continuation of the special values....
Kevin Buzzard (2001)
Journal de théorie des nombres de Bordeaux
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We give a down-to-earth introduction to the theory of families of modular forms, and discuss elementary proofs of results suggesting that modular forms come in families.
Haruzo Hida (1991)
Annales de l'institut Fourier
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Let be the Rankin product -function for two Hilbert cusp forms and . This -function is in fact the standard -function of an automorphic representation of the algebraic group defined over a totally real field. Under the ordinarity assumption at a given prime for and , we shall construct a -adic analytic function of several variables which interpolates the algebraic part of for critical integers , regarding all the ingredients , and as variables.
Haruzo Hida (1988)
Annales de l'institut Fourier
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Let and be holomorphic common eigenforms of all Hecke operators for the congruence subgroup of with “Nebentypus” character and and of weight and , respectively. Define the Rankin product of and by Supposing and to be ordinary at a prime , we shall construct a -adically analytic -function of three variables which interpolate the values for integers with by regarding all the ingredients , and as variables. Here is the Petersson...
Fernando Q. Gouvêa, Barry Mazur (1993)
Annales de l'institut Fourier
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We show that the coefficients of the characteristic power series of Atkin’s U operator acting on overconvergent -adic modular forms of weight vary -adically continuously as functions of . Are they in fact Iwasawa functions of ?