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THE TRANSFORMATION LAW AND trace formula ON THETA SERIES UNDER SIEGEL MODULAR GROUP

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Acta Mathematica Scientia 2008年第1期28卷 201-209页

作者：周海港陆洪文 Department of Mathematics Tongji University

The purposes of this article are to discuss the symplectic transformation laws on theta series and to give some explicit formulas for the trace of the symplectic operator.

关键词： theta series symplectic transformation law trace formula

A trace formula for Integro-differential Operators on the Finite Interval

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Acta Mathematicae Applicatae Sinica 2017年第1期33卷 141-146页

作者： Yu-ping WANG Hikmet Koyunbakan Chuan-fu YANG Department of Applied Mathematics Nanjing Forestry University Department of Mathematics Firat University Department of Applied Mathematics Nanjing University of Science and Technology

In this paper, we consider the eigenvalue problem for integro-differential operators with separated boundary conditions on the finite interval and find a trace formula for the integro-differential operator.

关键词： trace formula integro-differential operator eigenvalue

Stable local trace formula

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Science China Mathematics 2014年第12期57卷 2509-2518页

作者： PENG ZhiFeng Department of Mathematics Nanjing University

Langlands program is the central concern of modern number theory. In general, we think that the main tool for studying this program is the trace formula. Arthur-Selberg's trace formula is successful in solving the endoscopic case of Langlands program. Arthur stabilized the geometric side of the local trace formula in the general case, but did not stabilize the general spectral. This paper aims to solve the general case by different method in the Archimedean case, by directly stabilizing the spectral side of the local trace formula, and obtains the stable local trace formula.

关键词： Langlands program trace formula Arthur-Selberg's trace formula

Hill-Type formula and Krein-Type trace formula for Hamiltonian Systems

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Analysis in Theory and Applications 2021年第1期37卷 74-101页

作者： Xijun Hu Yuwei Ou Penghui Wang Hao Zhu School of Mathematics Shandong UniversityJinanShandong 250100China School of Mathematics(Zhuhai) Sun Yat-Sen UniversityZhuhaiGuangdong 519082China Department of Mathematics Nanjing UniversityNanjingJiangsu 210093China

In this paper,we give a survey on the Hill-type formula and its ***,we generalize the Hill-type formula for linear Hamiltonian systems and Sturm-Liouville systems with any self-adjoint boundary conditions,which include the standard Neumann,Dirichlet and periodic boundary *** Hill-type formula connects the infinite determinant of the Hessian of the action functional with the determinant of matrices which depend on the monodromy matrix and boundary ***,based on the Hill-type formula,we derive the Krein-type trace *** applications,we give nontrivial estimations for the eigenvalue problem and the relative Morse index.

关键词： Hill-type formula trace formula conditional Fredholm determinant relative Morse index

Asymptotic formulas of the Solutions and the trace formulas for the Polynomial Pencil of the Sturm-Liouville Operators

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Applied Mathematics 2016年第18期7卷 2411-2417页

作者： A. Adiloglu Nabiev Department of Mathematics Cumhuriyet University Sivas Turkey

This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.

关键词： Sturm-Liouville Equation Asymptotic formulas for Solutions Spectral Parameter Eigenvalue Boundary Value Problem trace formula Fractional Integrals and Derivatives

Isolation of the cuspidal spectrum:The function field case

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Science China Mathematics 2022年第7期65卷 1331-1342页

作者： Li Cai Bin Xu Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084China School of Mathematics Sichuan UniversityChengdu 610064China

Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula *** example,matrix coefficients of supercuspidal representations can be used as test functions for ***,they kill a large class of interesting cuspidal automorphic *** the case of number fields,multipliers of the Schwartz algebra are used in the recent work(see Beuzart-Plessis et al.(2021))to isolate all the cuspidal *** particular,they are suitable for the comparison of orbital *** multipliers are then applied to the proof of the Gan-Gross-Prasad conjecture for unitary groups(see Beuzart-Plessis et al.(2021,2022)).In this article,we prove the similar result on isolating the cuspidal spectrum in Beuzart-Plessis et al.(2021)for the function field case.

关键词： cuspidal spectrum Hecke algebra trace formula automorphic representation

Lefschetz formulae for p-Adic Groups

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Chinese Annals of Mathematics,Series B 2007年第4期28卷 463-474页

作者： Anton DEITMAR Mathematisches Institut Auf der Morgenstelle 10 72076 TübingenGermany.

In this paper, Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups. Applications lie in the realm of dynamical zeta functions.

关键词： Arithmetic groups trace formula Lefschetz formula

LOCALIZATION OPERATORS ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR

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Analysis in Theory and Applications 2005年第4期21卷 317-325页

作者： Jiman Zhao Beijing Normal University China

In this paper, we define the localization operator associated with the spherical mean operator, and show that the localization operator is not only bounded, but also in Schatten-Von Neumann class. We also give a trace... 详细信息

关键词： Wigner transform localization operator trace formula