The List of Hilbert’s Twenty-Three Problems: Hilbert’s Problem #11

Arbitrary Quadratic Forms: Solving quadratic forms with algebraic numerical coefficients

Hilbert’s 11th problem also concerns algebraic number fields. A quadratic form is an expression, like 

$x^2 + 2xy + y^2$ 

with integer coefficients in which each term has unknowns raised to a total degree of $2$. The number $9$ can be represented using integers in the above quadratic form — set x equal to 1 and y equal to $2$ — but the number $8$ cannot be represented by integers in that quadratic form. 

Some different quadratic forms can represent the same sets of whole numbers. Hilbert asked for a way to classify quadratic forms to determine whether two forms represent the same set of numbers. Some progress has been made, but the question is unresolved.

Πηγή: abakcus

📘

Έρχεται το πολλαπλό βιβλίο ΝΕΟ — βρες όλες τις επιλογές εδώ

PDF & Ψηφιακά Μαθησιακά Αντικείμενα — χωρίς εγγραφή • Portify

📚 437 βιβλία🎬 22.000+ Ψηφιακά Μαθησιακά Αντικείμενα

Δες τα βιβλία →