Spectral problems in geometry and arithmetic : NSF-CBMS Conference on Spectral Problems in Geometry and Arithmetic, August 18-22, 1997, University of Iowa
著者
書誌事項
Spectral problems in geometry and arithmetic : NSF-CBMS Conference on Spectral Problems in Geometry and Arithmetic, August 18-22, 1997, University of Iowa
(Contemporary mathematics, v. 237)
American Mathematical Society, c1999
大学図書館所蔵 全51件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references
内容説明・目次
内容説明
This work covers the proceedings of the NSF-CBMS Conference on 'Spectral Problems in Geometry and Arithmetic' held at the University of Iowa. The principal speaker was Peter Sarnak, who has been a central contributor to developments in this field. The volume approaches the topic from the geometric, physical, and number theoretic points of view. The remarkable new connections among seemingly disparate mathematical and scientific disciplines have surprised even veterans of the physical mathematics renaissance forged by gauge theory in the 1970s. Numerical experiments show that the local spacing between zeros of the Riemann zeta function is modelled by spectral phenomena: the eigenvalue distributions of random matrix theory, in particular the Gaussian unitary ensemble (GUE).Related phenomena are from the point of view of differential geometry and global harmonic analysis. Elliptic operators on manifolds have (through zeta function regularization) functional determinants, which are related to functional integrals in quantum theory. The search for critical points of this determinant brings about extremely subtle and delicate sharp inequalities of exponential type. This indicates that zeta functions are spectral objects - and even physical objects. This volume demonstrates that zeta functions are also dynamic, chaotic, and more.
目次
Connections between random matrices and Szego limit theorems by E. L. Basor On a fourth order curvature invariant by S.-Y. A. Chang and P. C. Yang Small eigenvalues of the Hodge Laplacian for three-manifolds with pinched negative curvature by R. Gornet and J. McGowan Heating and stretching Riemannian manifolds by C. M. Judge Number theory zeta functions and dynamical zeta functions by J. C. Lagarias Complex dimensions of fractal strings and oscillatory phenomena in fractal geometry and arithmetic by M. L. Lapidus and M. van Frankenhuysen High frequency cut-offs, trace formulas and geometry by K. Okikiolu Meromorphic continuation of the resolvent for Kleinian groups by P. Perry Variation of scattering poles for conformal metrics by Y. N. Petridis On Bilu's equidistribution theorem by R. Rumely Asymptotics of a class of Fredholm determinants by C. A. Tracy and H. Widom.
「Nielsen BookData」 より