Iwasawa Invariants.
Analytic formulas for the regulator of a number field.
Regulators and total positivity.
[Proceedings of the (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Hilbert symbols, class groups and quaternion algebras
Let be a quaternion algebra over a number field . To a pair of Hilbert symbols and for we associate an invariant in a quotient of the narrow ideal class group of . This invariant arises from the study of finite subgroups of maximal arithmetic kleinian groups. It measures the distance between orders and in associated to and If , we compute by means of arithmetic in the field The problem of extending this algorithm to the general case leads to studying a finite graph associated...
The finite subgroups of maximal arithmetic kleinian groups
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.
Raabe’s formula for -adic gamma and zeta functions
The classical Raabe formula computes a definite integral of the logarithm of Euler’s -function. We compute -adic integrals of the -adic -functions, both Diamond’s and Morita’s, and show that each of these functions is uniquely characterized by its difference equation and -adic Raabe formula. We also prove a Raabe-type formula for -adic Hurwitz zeta functions.
The arithmetic hyperbolic 3-manifold of smallest volume
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