topological polylogarithms and p adic interpolation of l values of totally real fields we develop the topological polylogarithm which provides an integral version of nori s eisenstein cohomology classes for mathrm gl n mathbb z and yields classes with values in an iwasawa algebra this implies directly the integrality properties of special values of l functions of totally real fields and a construction of the associated p adic l function using a result of graf we also apply this to prove some integrality and p adic interpolation results for the eisenstein cohomology of hilbert modular varieties

nonreal eigenvalues for second order differential operators on networks with circuits it is shown that on every finite network with at least one circuit there exist second order differential operators having an infinite number of nonreal eigenvalues the presence of nonreal eigenvalues implies that these operators cannot be selfadjoint with respect to any metric these eigenvalues reveal also the existence of oscillatory solutions for the corresponding time dependent partial differential equations

values of zeta functions at negative integers dedekind sums and toric geometry in the present paper we study relations among special values of zeta functions of real quadratic fields properties of generalized dedekind sums and todd classes of toric varieties the main theme of the paper is the use of toric geometry to explain in a conceptual way properties of the values of zeta functions and dedekind sums as well as to provide explicit computations both toric varieties and zeta functions associate numerical invariants to cones in lattices with different motivations and applications though we will focus on the case of two dimensional cones in the present paper we introduce notation and definitions that are valid for cones of arbitrary dimension the reason for this added generality is clarity as well as preparation for the results of a subsequent publication

nonparametric analysis for doubly ordered two way contingency tables tsujitani 1992 biometrics 48 267 269 and kateri 1993 biometrics 49 950 951 considered analyses for two way contingency tables in this reader reaction a nonparametric analysis using mnidrank scores is given this analysis can be interpreted in terms of bivariate moments does not make model assumptions takes into account the ordinal nature of the data and allows monte carlo p values to be given

sommes de dedekind associees a un corps de nombres totalement reel we define dedekind sums attached to a totally real number field of class number one we prove that they satisfy some reciprocity law then we relate them to special values of hecke l functions we conclude that they are ruled by stark s conjecture

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

the analysis of nonadditivity in two way analysis of variance abstract singular value decompositions are used to study interactions in two way layouts in contrast to traditional treatments emphasis is on description of the nature of the interactions rather than on tests of whether they do or do not exist the first model considered assumes that the matrix of interactions has rank 1 so in a singular value decomposition of the interactions only one singular value is not 0 given that this model holds and interactions are present normal approximations are obtained under conditions described for the estimates of this singular value and for the corresponding scores for row categories and column categories thus approximate confidence intervals can be obtained for the parameters in this singular value decomposition of interactions in addition under this model approximate t and f tests can be constructed for hypotheses that assign specified values to the row and column scores in the singular value decomposition results are illustrated in a reanalysis of data previ

a polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed we prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d dimensional euclidean space previously such algorithms were known for dimensions d 1 2 3 and 4 only

parametric bootstrap methods for testing multiplicative terms in gge and ammi models the genotype main effects and genotype by environment interaction effects gge model and the additive main effects and multiplicative interaction ammi model are two common models for analysis of genotype by environment data these models are frequently used by agronomists plant breeders geneticists and statisticians for analysis of multi environment trials in such trials a set of genotypes e g crop cultivars are compared across a range of environments e g locations the gge and ammi models use singular value decomposition to partition genotype by environment interaction into an ordered sum of multiplicative terms this article deals with the problem of testing the significance of these multiplicative terms in order to decide how many terms to retain in the final model we propose parametric bootstrap methods for this problem models with fixed main effects fixed multiplicative terms and random normally distributed errors are considered two methods are derived a full and a simple parametric bootstrap method these are compared with the alternatives of using approximate f tests and cross validation in a simulation study based on four multi environment trials both bootstrap methods performed well with regard to type i error rate and power the simple parametric bootstrap method is particularly easy to use since it only involves repeated sampling of standard normally distributed values this method is recommended for selecting the number of multiplicative terms in gge and ammi models the proposed methods can also be used for testing components in principal component analysis

q dedekind type sums related to q zeta function and basic l series abstract the main purpose of this paper is to define new generating functions by applying the mellin transformation formula to these generating functions we define q analogue of riemann zeta function q analogue hurwitz zeta function q analogue dirichlet l function and two variable q l function in particular by using these generating functions we will construct new generating functions which produce q dedekind type sums and q dedekind type sums attached to dirichlet character we also give the relations between these sums and dedekind sums furthermore by using product which is given in this paper we will give the relation between dedekind sums and q l function as well

a note on the additive and multiplicative models in two way contingency tables summary another look at the mandel type least squares fitting of a mixed additive and multiplicative model is discussed for the analysis of two way contingency tables the method is carried out by a two stage process i fit the additive part of the model then take residuals and ii fit the multiplicative part to the residuals

higher kronecker limit formulas for real quadratic fields for every integer kf 2 we introduce an analytic function of a positive real variable and give a universal formula expressing the values z b k of the zeta func tions of narrow ideal classes in real quadratic fields in terms of this function and its deriva tives up to order k 1 evaluated at reduced real quadratic irrationalities associated to b we show that our functions satisfy functional equations and use these to deduce explicit formulas for the rational numbers z b 1 k we also give an interpretation of our for mula for z b k in terms of cohomology groups of sl 2 z with analytic coe cients and describe a twisted extension of the main formula that allows one to treat zeta values of zeta functions of ray classes rather than just ideal classes finally we use our formulas to compute some zeta values numerically and test that they are expressible as combinations of higher polylogarithm functions evaluated at algebraic arguments

on complex zeros off the critical line for non monomial polynomial of zeta functions in this paper we show that any polynomial of zeta or l functions with some conditions has infinitely many complex zeros off the critical line this general result has abundant applications by using the main result we prove that the zeta functions associated to symmetric matrices treated by ibukiyama and saito certain spectral zeta functions and the euler zagier multiple zeta functions have infinitely many complex zeros off the critical line moreover we show that the lindelof hypothesis for the riemann zeta function is equivalent to the lindelof hypothesis for zeta functions mentioned above despite of the existence of the zeros off the critical line next we prove that the barnes multiple zeta functions associated to rational or transcendental parameters have infinitely many zeros off the critical line by using this fact we show that the shintani multiple zeta functions have infinitely many complex zeros under some conditions as corollaries we show that the mordell multiple zeta functions the euler zagier hurwitz type of multiple zeta functions and the witten multiple zeta functions have infinitely many complex zeros off the critical line

a characteristic equation associated to an eigenvalue problem on c2 networks abstract a characteristic equation for the spectrum of an eigenvalue problem on c 2 networks is deduced and those special cases are investigated in which the spectrum depends mainly on the structure of the abstract graph belonging to the c 2 network

multiplicity of solutions of second order linear differential equations on networks abstract an upper optimal bound is obtained for the multiplicity of solutions of second order linear differential equations on networks with general boundary and node conditions this bound depends only on the abstract topological associated graph in particular the result holds for the multiplicity of eigenvalues of the corresponding operators