Search Results

Unfortunately I never found a good reference book for the adeles and ideles definitions and properties : they always are treated in appendix or in a little chapter giving most of the time only the necessary … Travelling among tens of lecture notes and books (Weil, Vignéras, Goldfeld, Lang, Milne, Tate, Bump, Gelbart, etc. : all books which have not adeles as main theme !) …

For a quaternion algebra $D$, introduce the quaternionic similitude unitary groups: \begin{equation} \mathrm{GU}_D = \left\{ g \in \mathrm{GL}(D) \ : \ g^\star \left( \begin{array}{cc} & 1 \\ 1 & \en …

Let $F$ be a (totally real) number field, and $E$ a (totally imaginary) quadratic extension of $F$. We consider $U$ a unitary group (with respect to a given hermitian form over $E$). The question is: …

say Schwartz-Bruhat) function, the following identity holds : $$\int_{\mathbf{A}^2} f(x)dx = \int_{SL_2(\mathbf{A})/SL_2(K)} \left( \sum_{a \in K^2 - 0} f(ua) \right) du$$ where $\mathbf{A}$ are the adeles …

Let $K$ be a quadratic number field. I am struggling with some "usual" maps in algebraic number theory, but with which I am not used to, confusing a lot of different settings, as idèles, correspondin …