关于Heisenberg流形Weyl律的余项(Ⅱ)
摘要
研究(2l+1)维无理Heisenberg流形上Weyl律余项的平方积分均值,并得到了渐近公式.
出处
《中国科学(A辑)》
CSCD
北大核心
2008年第10期1135-1152,共18页
Science in China(Series A)
基金
国家自然科学基金(批准号:10771127)资助项目
参考文献29
-
1Hormander L. The spectral function of an elliptic operator. Acta Math, 121:193-218 (1968)
-
2Bentkus V, Gotze F. Lattice point problems and distribution of values of quadratic forms. Ann Math, 50(2): 977-1027 (1999)
-
3Berard P H. On the wave equation on a compact Riemannian manifold without conjugate points. Math Z, 155(3): 249-276 (1977)
-
4Bleher L. On the distribution of the number of lattice points inside a family of convex ovals. Duke Math J, 67(3): 461-481 (1992)
-
5Chung D, Petridis Y N, Toth J, The remainder in Weyl's law for Heisenberg manifolds Ⅱ. Bonner Mathematische Schriften, Nr 360, Bonn, 2003, 16
-
6Fricker F. Einfuhrung in die Gitterpunketlehre, [Introduction to lattice point theory] Lehrbucher und Monographien aus dem Gebiete der Exakten Wissenschaften(LMW). Mathematische Reihe[Textbooks and Monographs in the Exact Sciences]73. Basel-Boston-Mas: Birkhauser Verlag, 1982
-
7Gotze F. Lattice point problems and values of quadratic forms. Invent Math, 157:195-226 (2004)
-
8Huxley M N. Exponential sums and lattice points Ⅲ. Proc London Math Soc, 87(3): 591-609 (2003)
-
9Ivrii V Y. Precise Spectral Asymptotics for Elliptic Operators Acting in Fibrings over Manifolds with Boundary. Lecture Notes in Mathematics, Vol 1100, New York: Springer, 1984
-
10Khosravi M, Petridis Y. The remainder in Weyl's law for n-dimensional Heisenberg manifolds. Proc Amer Math Soc, 133:3561-3571 (2005)
-
1邓俊兰.广义高维Cochrane和的上界估计[J].纺织高校基础科学学报,2014,27(1):58-64.
-
2史美华.与Dedekind函数ψ(n)有关的误差项估计[J].浙江大学学报(理学版),2001,28(5):478-482. 被引量:1
-
3王佳,翟文广.(a,a,b)型三维除数问题余项的平方积分均值(英文)[J].数学进展,2011,40(5):549-566.
-
4何杰铃,魏凌,杨金生,李喜琪,何益,张雨东.光瞳半径对纯位相调制激光束整形系统的影响[J].物理学报,2016,65(4):339-348.