http://web.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
Extra Form
강연자 David Leep
소속 Univ. of Kentucky
date 2011-03-17

It is usually a difficult problem to characterize precisely which elements of a given integral domain can be written as a sum of squares of elements from the integral domain. Let R denote the ring of integers in a quadratic number field. This talk will deal with the problem of identifying which elements of R can be written as a sum of squares. If an element in R can be written as a sum of squares, then the element must be totally positive. This necessary condition is not always sufficient. We will determine exactly when this necessary condition is sufficient. In addition, we will develop several criteria to guarantee that a representation as a sum of squares is possible. The results are based on theorems of I. Niven and C. Siegel from the 1940's, and R. Scharlau from 1980.

Atachment
첨부 '1'
  1. 01Apr
    by 김수현
    in 수학강연회

    A dissipative effect on some PDEs with physical singularity

  2. 07Nov
    by Editor
    in 수학강연회

    Hamiltonian dynamics, Floer theory and symplectic topology

  3. 26Sep
    by 김수현
    in 수학강연회

    Idempotents and topologies

  4. 07Nov
    by Editor
    in 수학강연회

    Brownian motion with darning and conformal mappings

  5. 23Mar
    by 김수현
    in 수학강연회

    Anomalous diffusions and fractional order differential equations

  6. 01Nov
    by Manager
    in 수학강연회

    Unprojection

  7. 25Apr
    by 김수현
    in 수학강연회

    Iwahori-Hecke algebras and beyond

  8. 10Oct
    by 김수현
    in 수학강연회

    Seifert fiberings

  9. 26Oct
    by 김수현
    in 수학강연회

    Weak and strong well-posedness of critical and supercritical SDEs with singular coefficients

  10. 11Sep
    by 김수현
    in 수학강연회

    Nonlocal generators of jump type Markov processes

  11. 18Apr
    by 김수현
    in 수학강연회

    Unique ergodicity for foliations

  12. 07Nov
    by Editor
    in 수학강연회

    It all started with Moser

  13. 07Nov
    by Editor
    in 수학강연회

    Conservation laws and differential geometry

  14. 07May
    by 김수현
    in 수학강연회

    Number theoretic results in a family

  15. 07Nov
    by Editor
    in 특별강연

    Queer Lie Superalgebras

  16. 07Nov
    by Editor
    in 수학강연회

    학부생을 위한 강연: A COMBINATORIAL FORMULA FOR INFORMATION FLOW IN A NETWORK

  17. 07Nov
    by Editor
    in 수학강연회

    Sums of squares in quadratic number rings

  18. 07Nov
    by Editor
    in 수학강연회

    Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms

  19. 07Nov
    by Editor
    in 수학강연회

    Topology and number theory

  20. 26May
    by 김수현
    in 수학강연회

    Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

Board Pagination Prev 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Next
/ 15