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Raabe’s formula for p -adic gamma and zeta functions

Henri Cohen, Eduardo Friedman (2008)

Annales de l’institut Fourier

The classical Raabe formula computes a definite integral of the logarithm of Euler’s Γ -function. We compute p -adic integrals of the p -adic log Γ -functions, both Diamond’s and Morita’s, and show that each of these functions is uniquely characterized by its difference equation and p -adic Raabe formula. We also prove a Raabe-type formula for p -adic Hurwitz zeta functions.

Ramification and moduli spaces of finite flat models

Naoki Imai (2011)

Annales de l’institut Fourier

We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud’s theorem on the uniqueness of finite flat models in low ramifications.

Ramification groups in Artin-Schreier-Witt extensions

Lara Thomas (2005)

Journal de Théorie des Nombres de Bordeaux

Let K be a local field of characteristic p > 0 . The aim of this paper is to describe the ramification groups for the pro- p abelian extensions over K with regards to the Artin-Schreier-Witt theory. We shall carry out this investigation entirely in the usual framework of local class field theory. This leads to a certain non-degenerate pairing that we shall define in detail, generalizing in this way the Schmid formula to Witt vectors of length n . Along the way, we recover a result of Brylinski but with...

Ramification in quartic cyclic number fields K generated by x 4 + p x 2 + p

Julio Pérez-Hernández, Mario Pineda-Ruelas (2021)

Mathematica Bohemica

If K is the splitting field of the polynomial f ( x ) = x 4 + p x 2 + p and p is a rational prime of the form 4 + n 2 , we give appropriate generators of K to obtain the explicit factorization of the ideal q 𝒪 K , where q is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.

Rational base number systems for p-adic numbers

Christiane Frougny, Karel Klouda (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.

Rational base number systems for p-adic numbers

Christiane Frougny, Karel Klouda (2012)

RAIRO - Theoretical Informatics and Applications

This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.

Relative Bogomolov extensions

Robert Grizzard (2015)

Acta Arithmetica

A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of K × has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of L × ∖ K × . We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.

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