6533b7defe1ef96bd1275db6

RESEARCH PRODUCT

Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern

Horst Pfeuffer

subject

Discrete mathematicsPure mathematicsAlgebra and Number TheoryQuadratic equationBounded functionBinary quadratic formField (mathematics)Quadratic fieldAlgebraic numberCongruence relationFinite setMathematics

description

Abstract It is proved that totally positive quadratic forms with three or more variables and class number h = 1 exist only in a finite number of algebraic number fields. Each field allows only a finite number of such forms with bounded scale. To prove this, upper estimates for all local factors in Siegel's analytic formula are constructed by calculating explicitly numbers of solutions of quadratic congruences.

yearjournalcountryeditionlanguage
1971-11-01Journal of Number Theory
https://doi.org/10.1016/0022-314x(71)90011-4