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$p$ -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 analysis and Bell numbers of two variables. (Analyse $p$ -adique et nombres de Bell à deux variables.)

Mazouz, Abdelhak (1996)

Bulletin of the Belgian Mathematical Society - Simon Stevin

$p$ -adic chaos and random number generation.

Woodcock, Christopher F., Smart, Nigel P. (1998)

Experimental Mathematics

$p$ -adic dynamical systems and formal groups

Hua-Chieh Li (1996)

Compositio Mathematica

$p$ -adic Fourier theory.

Schneider, P., Teitelbaum, J. (2001)

Documenta Mathematica

$p$ -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.

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

Pierre Colmez, Leila Schneps (1992)

Compositio Mathematica

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

Kenneth A. Ribet (1977/1978)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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

Pierrette Cassou-Noguès (1980)

Compositio Mathematica

$p$ -adic $L$ -functions for modular forms

Shai Haran (1987)

Compositio Mathematica

$p$ -adic $L$ -functions of Hilbert modular forms

Andrzej Dabrowski (1994)

Annales de l'institut Fourier

We construct $p$ -adic $L$ -functions (in general case unbounded) attached to “motivic" primitive Hilbert cusp forms as a non-archimedean Mellin transform of the corresponding admissible measure. In order to prove the growth conditions of the appropriate complex-valued distributions we represent them as Rankin type representation and use Atkin–Lehner theory and explicit form of Fourier coefficients of Eisenstein series.

Currently displaying 1 – 20 of 65

Page 1 Next

Displaying 1 – 20 of 65

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

$p$ -adic analysis and Bell numbers of two variables. (Analyse $p$ -adique et nombres de Bell à deux variables.)

$p$ -adic chaos and random number generation.

$p$ -adic dynamical systems and formal groups

$p$ -adic Fourier theory.

$p$ -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

$p$ -adic $L$ -functions for modular forms

$p$ -adic $L$ -functions of Hilbert modular forms

$p$ -adic representations arising from descent on abelian varieties

$p$ -adic representations of a local field. (Représentations $p$ -adiques d'un corps local.)

$p$ -адические ряды Гекке мнимых квадратичных полей

P-Acid Fields Having the Same Type of Algebraic Extensions.

p-Adic Congruences and Modular Forms of Half Integer Weight.

p-Adic Congruences for Cycle Integrals Associated to Elliptic Curves with Complex Multiplication.

p-adic Dedekind sums.

p-adic Distributions Associated to Heegner Points on Modular Curves.

p-adic height pairings. II.

Currently displaying 1 – 20 of 65