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Displaying 101 – 120 of 181

On the classgroups of imaginary abelian fields

David Solomon (1990)

Annales de l'institut Fourier

Let $p$ be an odd prime, $χ$ an odd, $p$ -adic Dirichlet character and $K$ the cyclic imaginary extension of $Q$ associated to $χ$ . We define a “ $χ$ -part” of the Sylow $p$ -subgroup of the class group of $K$ and prove a result relating its $p$ -divisibility to that of the generalized Bernoulli number $B_{1, χ^{- 1}}$ . This uses the results of Mazur and Wiles in Iwasawa theory over $Q$ . The more difficult case, in which $p$ divides the order of $χ$ is our chief concern. In this case the result is new and confirms an earlier conjecture of G....

On the cyclotomic invariants of Iwasawa.

Tauno Metsänkylä (1975)

Mathematica Scandinavica

On the degree of a local zeta function

Diane Meuser (1987)

Compositio Mathematica

On the Factorization of p-adic L-series.

Benedict H. Gross (1980)

Inventiones mathematicae

On the Functional Equation of the Artin L-Function for Characters of Real Representations.

A. Fröhlich, J. Queyrut (1973)

Inventiones mathematicae

On the generalized Bernoulli numbers that belong to unequal characters.

Ilya Sh. Slavutskii (2000)

Revista Matemática Iberoamericana

The study of class number invariants of absolute abelian fields, the investigation of congruences for special values of L-functions, Fourier coefficients of half-integral weight modular forms, Rubin's congruences involving the special values of L-functions of elliptic curves with complex multiplication, and many other problems require congruence properties of the generalized Bernoulli numbers (see [16]-[18], [12], [29], [3], etc.). The first steps in this direction can be found in the papers of...

On the ?-invariant of the ?-transform of a rational function.

W. Sinnott (1984)

Inventiones mathematicae

On the power series attached to p-adic L-functions.

W. Sinnott (1987)

Journal für die reine und angewandte Mathematik

On the proof of Humbert's volume formula.

Fritz Grunewald, Stefan Kühnlein (1998)

Manuscripta mathematica

On the Rationality of Certain Generating Functions.

Diane Meuser (1981)

Mathematische Annalen

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

Haruzo Hida (1996)

Mémoires de la Société Mathématique de France

On the values of p-adic L-functions at positive integers

Jack Diamond (1979)

Acta Arithmetica

On Values of Zeta Functions and ?-adic Euler Characteristc.

Jürgen Neukirch, Pilar Bayer (1978/1979)

Inventiones mathematicae

On zeroes of the twisted tensor L-function.

Yuval Z. Flicker (1993)

Mathematische Annalen

Overconvergent modular symbols and $p$ -adic $L$ -functions

Robert Pollack, Glenn Stevens (2011)

Annales scientifiques de l'École Normale Supérieure

This paper is a constructive investigation of the relationship between classical modular symbols and overconvergent $p$ -adic modular symbols. Specifically, we give a constructive proof of acontrol theorem (Theorem 1.1) due to the second author [19] proving existence and uniqueness of overconvergent eigenliftings of classical modular eigensymbols of non-critical slope. As an application we describe a polynomial-time algorithm for explicit computation of associated $p$ -adic $L$ -functions in this case. In...

$p$ -adic Abelian Stark conjectures at $s = 1$

David Solomon (2002)

Annales de l’institut Fourier

A $p$ -adic version of Stark’s Conjecture at $s = 1$ is attributed to J.-P. Serre and stated (faultily) in Tate’s book on the Conjecture. Building instead on our previous paper (and work of Rubin) on the complex abelian case, we give a new approach to such a conjecture for real ray-class extensions of totally real number fields. We study the coherence of our $p$ -adic conjecture and then formulate some integral refinements, both alone and in combination with its complex analogue. A ‘Weak Combined Refined’ version...

$p$ -adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups

John L. Boxall (1986)

Annales de l'institut Fourier

The purpose of this paper is to generalize, to certain commutative formal groups of dimension one and height greater than one defined over the ring of integers of a finite extension of $Q_{p}$ , some results on $p$ -adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group ${\hat{G}}_{m}$ , and which they used to construct $p$ -adic $L$ -functions.

Currently displaying 101 – 120 of 181

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Displaying 101 – 120 of 181

On the classgroups of imaginary abelian fields

On the cyclotomic invariants of Iwasawa.

On the degree of a local zeta function

On the Factorization of p-adic L-series.

On the Functional Equation of the Artin L-Function for Characters of Real Representations.

On the generalized Bernoulli numbers that belong to unequal characters.

On the ?-invariant of the ?-transform of a rational function.

On the power series attached to p-adic L-functions.

On the proof of Humbert's volume formula.

On the Rationality of Certain Generating Functions.

On the search of genuine $p$ -adic modular $L$ -functions for $G L (n)$ . With a correction to: On $p$ -adic $L$ -functions of $G L (2) \times G L (2)$ over totally real fields

On the values of p-adic L-functions at positive integers

On Values of Zeta Functions and ?-adic Euler Characteristc.

On zeroes of the twisted tensor L-function.

Overconvergent modular symbols and $p$ -adic $L$ -functions

$p$ -adic Abelian Stark conjectures at $s = 1$

$p$ -adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups

$p$ -adic interpolation of special values of Hecke L-functions

$p$ -adic $L$ -functions attached to characters of $p$ -power order

$p$ -adic $L$ -functions for elliptic curves with complex multiplication I

Currently displaying 101 – 120 of 181