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401-3370-17L 4 Credits BSC , MSC D-MATH

Arithmetic of Quadratic Forms

Lecturers & Examiners: PD Dr. Menny Akka Ginosar
Number of participants limited to 12. Registration to this seminar is closed, the participants have been selected. There is no waiting list.
VVZ CR n/a

Last Updated: 2026-02-05 16:06:49

Abstract

Introductory seminar about rational quadratic forms. P-adic numbers, Hasse's local to global principle and the finiteness of the genus will be discussed.

Objective

Quadratic forms and the numbers they represent have been of interest to mathematicians for a long time. For example, which integers can be expressed as a sum of two squares of integers? Or as a sum of three squares? Lagrange's four-squares theorem for instance states that any positive integer can be expressed as a sum of four squares. Such questions motivated the development of many aspects of algebraic number theory. In this seminar we follow the beautiful monograph of Cassels "Rational quadratic forms" and will treat the fundamental results concerning quadratic forms over the integers and the rationals such as Hasse's local to global principle and finiteness of the genus.

Content

The seminar will mostly follow the book "Rational quadratic forms" by J.W.S. Cassels, particularly Chapters 1-9. Exercises in this book are an integral part of the seminar. Towards the end of the semester additional topics may be treated.

Resources

Lecture Notes

Cassels, John William Scott. Rational quadratic forms. Vol. 13. Academic Pr, 1978.

Literature

Main reference: Cassels, John William Scott. Rational quadratic forms. Vol. 13. Academic Pr, 1978. Additional references: Kitaoka, Yoshiyuki. Arithmetic of quadratic forms. Vol. 106. Cambridge University Press, 1999. Schulze-Pillot, Rainer. "Representation by integral quadratic forms - a survey." Contemporary Mathematics 344 (2004): 303-322.

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC

Examination

Type
ungraded semester performance

Registration & Places

Limited places (Special selection)
Signup Start
03.01.2022
Signup End
18.02.2022

Course Components

Type Title Time & Place Hours
seminar Arithmetic of Quadratic Forms
  • Mon 12:15-14:00 (HG G 26.3)
2 h weekly

Offered In

  • Mathematics Bachelor
    • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester.)
  • Mathematics Master
    • Seminars and Semester Papers
      • Seminars (NOTICE: The number of seminar places is limited, and the special selection procedure should help to allocate the places not primarily according to the registration time. Everybody is waitlisted first when he/she tries to register for a seminar in myStudies. Moreover: Only one mathematics seminar can be chosen per semester. In case you need to attend 2 seminars in this semester, please take contact with the Study Administration (email: ).)