heights of heegner cycles and derivatives of l series 0 introduction 99 1 intersections and heights 103 2 kuga sato varieties and cm cycles 117 3 heights of cm cycles 124 4 heights of heegner cycles 137 5 proof of the main identity and the consequences 147 references 151

non vanishing of high derivatives of automorphic l functions at the center of the critical strip keywords modular l functions mollification nonvanishing results central value of high derivatives analytic rank jacobian variety reference tan article 2000 004doi 10 1515 crll 2000 074 record created on 2008 11 14 modified on 2017 05 12

on the central value of symmetric square l functions let s k n be the space of cusp forms of weight k level n and character for f in s k n chi let l s sym2 f be the symmetric square l function and l s f otimes f be the rankin selberg square attached to f for fixed k 2 n prime and real primitive asymptotic formulas for the first and second moment of the central value of l s sym2 f and l s f otimes f over a basis of s k n are given as n as an application it is shown that a positive proportion of the central values l 1 2 sym2 f does not vanish

on central l derivative values of automorphic forms we study the average and nonvanishing of the central l derivative values of l s f and l s f k scriptscriptstyle d for f in an orthogonal hecke eigenbasis mathcal h 2k of weight 2k cusp forms of level 1 for large odd k here f k scriptscriptstyle d is the base change of f to an imaginary quadratic field k scriptscriptstyle d mathbb q sqrt d with fundamental discriminant d we prove asymptotic formulas for the first and second moments of l frac 1 2 f as well as the first moment of l frac 1 2 f k scriptscriptstyle d over mathcal h 2k as odd k rightarrow infty further we employ mollifiers to establish that for sufficiently large k there are positive proportion of hecke eigenforms f in mathcal h 2k with l frac 1 2 f ne 0 we also give applications of our results to heegner cycles of high weights of the modular curve x 0 1

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

on regularizing singular systems by decentralized output feedback this paper considers linear time invariant decentralized singular systems which are either nonregular or if they are regular they have impulsive modes it derives algebraic necessary and sufficient conditions for making a singular system both regular and impulse free by decentralized output feedback control laws and decentralized proportional plus derivative output feedback control laws

demography of cirsium vulgare in a grazing experiment the complete demographies of 16 populations of cirsium vulgare were followed in a replicated experiment the experiment was a factorial combination of two intensities of sheep grazing in each of three seasons winter grazed or ungrazed spring grazed or ungrazed and summer light or heavy grazing giving eight treatments in two blocks for 6 years from 1987 to 1992 the population sizes of c vulgare were monitored in each of the 16 paddocks after 1989 grazing in spring or winter or increased grazing in summer all increased population sizes population sizes fluctuated widely between years the effects of the grazing treatments and plant sizes on the transitions between nine life history stages were determined

a two dimensional helmhotlz equation solution for the multiple cavity scattering problem here considered is the mathematical analysis and numerical computation of the electromagnetic wave scattering by multiple cavities embedded in an infinite ground plane above the ground plane the space is filled with a homogeneous medium while the interiors of the cavities are filled with inhomogeneous media characterized by variable permittivities by introducing a new transparent boundary condition on the cavity apertures the multiple cavity scattering problem is reduced to a boundary value problem of the two dimensional helmholtz equation imposed in the separated interior domains of the cavities the existence and uniqueness of the weak solution for the model problem is achieved via a variational approach a block gauss seidel iterative method is introduced to solve the coupled system of the multiple cavity scattering problem where only a single cavity scattering problem is required to be solved at each iteration numerical examples demonstrate the efficiency and accuracy of the proposed method

eigenstructure assignment in descriptor systems coordinate free conditions are given for pole assignment by feedback in linear descriptor singular systems which guarantee closed loop regularity these conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback

minimum norm regularization of descriptor systems by mixed output feedback we study the regularization problem for linear constant coefficient descriptor systems ex ax bu y1 cx y2 x by proportional and derivative mixed output feedback necessary and sufficient conditions are given which guarantee that there exist output feedbacks such that the closed loop system is regular has index at most one and e bg has a desired rank i e there is a desired number of differential and algebraic equations to resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of e is decreased numerical procedures are derived to construct the desired feedback gains these numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way

technical communique regularizability of linear time invariant descriptor systems under decentralized control regularizability conditions for linear time invariant descriptor systems under decentralized output feedback are presented in this paper the regularizability is characterized by rank conditions that involve the original system matrices only new rank conditions for regularity of the system are also derived

nonvanishing of central l values of maass forms abstract with the method of moments and the mollification method we study the central l values of gl 2 maass forms of weight 0 and level 1 and establish a positive proportional nonvanishing result of such values in the aspect of large spectral parameter in short intervals which is qualitatively optimal in view of weyl s law as an application of this result and a formula of katok sarnak we give a nonvanishing result on the first fourier coefficients of maass forms of weight 1 2 and level 4 in the kohnen plus space

on regularizing descriptor systems by output feedback in this paper linear time invariant descriptor variable systems are considered which are either nonregular or if they are regular they have impulsive modes it is shown that if a certain necessary and sufficient condition is satisfied then both regularity can be established and impulsive modes can be eliminated by output feedback we have also considered the problem of achieving structural properties of the regularized system

rankin selberg l functions in the level aspect keywords moments rankin selberg convolution level aspect convexity breaking reference tan article 2002 003doi 10 1215 s0012 7094 02 11416 1 record created on 2008 11 14 modified on 2017 05 12

algebraic properties of singular systems subject to decentralized output feedback this paper investigates algebraic properties of decentralized singular systems dsss under local static output feedback new concepts of the geometric multiplicity gm of the finite decentralized fixed mode dfm the decentralized output feedback variable polynomial dvp and the finite decentralized output feedback cycle index dci of the dss are defined the formulas for determining the gm and the dci are given in terms of the dfm and the system matrices it is shown that almost any decentralized output feedback can make the zeros of the dvp i e the closed loop poles that are variable distinct and away from any given finite set in the complex plane it is also shown that the finite dfm of the dss are those uncontrollable and or observable finite modes of the closed loop dss through any single channel finally the minimal number of the inputs and outputs that guarantee the finite modes of the closed loop dss controllable and observable is shown to be the finite dci of the dss an illustrative example is provided

nonvanishing of the central l values with large weight abstract in this paper we establish an optimal nonvanishing result for the central l values of holomorphic cuspidal hecke eigenforms with large individual weight

on the regularizability of singular systems the property of regularity of singular systems is not a feedback invariant to correct this deficiency a new property of regularizability is defined and geometric tests are given for it in terms of system matrices regularizability is shown to be the natural extension of regularity which is a condition on the homogeneous system to controlled singular systems definitions of controllability and reachability are modified depending on regularizability rather than regularity a brief comparison of proportional and proportional plus derivative feedback laws in the context of making the closed loop system regular regular and reachable and regular and controllable is also given dynamical interpretations of these properties are also presented

mollification of the fourth moment of automorphic l functions and arithmetic applications we compute the asymptotics of twisted fourth power moments of modular l functions of large prime level near the critical line this allows us to prove some new non vanishing results on the central values of automorphic l functions in particular those obtained by base change from gl 2 q to gl 2 k for k a cyclic field of low degree

a density theorem on automorphic l functions and some applications we establish a density theorem of automorphic l functions and give some applications on the extreme values of these l functions at s 1 and the distribution of the hecke eigenvalue of holomorphic cusp forms contents