Such equations have an interesting history. In art. 358 of the Disquisitiones [1, a], Gauss determines the Gaussian sums (the so-called cyclotomic “periods”) of order 3, for a prime of the form p =… Expand

I. Elementary Theory.- I. Locally compact fields.- 1. Finite fields.- 2. The module in a locally compact field.- 3. Classification of locally compact fields.- 4. Structure of p-fields.- II. Lattices… Expand

I EISENSTEIN.- I Introduction.- II Trigonometric functions.- III The basic elliptic functions.- IV Basic relations and infinite products.- V Variation I.- VI Variation II.- II KRONECKER.- VII Prelude… Expand

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I. Preliminaries on Adele-Geometry.- 1.1. Adeles.- 1.2. Adele-spaces attached to algebraic varieties.- 1.3. Restriction of the basic field.- II. Tamagawa Measures.- 2.1. Preliminaries.- 2.2. The case… Expand

Algebraic preliminaries Algebraic theory of specializations Analytic theory of specializations The geometric language Intersection-multiplicities (special case) General intersection-theory The… Expand