Links between cyclotomic and Iwasawa theory.
Links between and character sums
We express , as defined in the title, for and prime in terms of values of characters modulo . Using this, we show that the universal lower bound for can, in general, be substantially improved when is composed of primes lying in a fixed residue class modulo . We also prove a corresponding improvement when is the product of the first s primes for infinitely many natural numbers .
L'invariant de Witt de la forme Tr(x2).
List of Paul Erdős's publications in number theory
Liste der Publikationen von Martin Eichler
Ljunggren's Diophantine problem connected with virus structure.
Local and canonical heights of subvarieties
Classical results of Weil, Néron and Tate are generalized to local heights of subvarieties with respect to hermitian pseudo-divisors. The local heights are well-defined if the intersection of supports is empty. In the archimedean case, the metrics are hermitian and the local heights are defined by a refined version of the -product of Gillet-Soulé developped on compact varieties without assuming regularity. In the non-archimedean case, the local heights are intersection numbers using methods from...
Local behaviour of a class of multiplicative functions
Local Borcherds products
The local Picard group at a generic point of the one-dimensional Baily-Borel boundary of a Hermitean symmetric quotient of type is computed. The main ingredient is a local version of Borcherds’ automorphic products. The local obstructions for a Heegner divisor to be principal are given by certain theta series with harmonic coefficients. Sometimes they generate Borcherds’ space of global obstructions. In these particular cases we obtain a simple proof of a result due to the first author: Suppose...
Local Class Field Theory via Lubin-Tate Theory
We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].
Local coefficients and normalization of intertwining operators for
Local conditions for global representations of quadratic forms
Local constant of Ind...1.
Local Diophantine Properties of Shimura Curves.
Local global theorems for diagonal forms of higher degree.
Local height functions and the Mordell-Weil theorem for Drinfeld modules
Local heights on Abelian varieties and rigid analytic uniformization.
Local heights on Galois covers of the projective line
Local Indecomposability of Hilbert Modular Galois Representations
We prove the indecomposability of the Galois representation restricted to the -decomposition group attached to a non CM nearly -ordinary weight two Hilbert modular form over a totally real field under the assumption that either the degree of over is odd or the automorphic representation attached to the Hilbert modular form is square integrable at some finite place of .
Local Leopoldt's problem for rings of integers in Abelian -extensions of complete discrete valuation fields.