errata and comments on orthogonal moments based on exponent functions in this paper we show that the exponent fourier moments efms as defined in ref 1 are imprecise and the radial function of efms performs numerically unstable at last an improvement of exponent fourier moments iefms is given for avoiding the above problems experimental results also show the superiority of the proposed methods the imprecisions of exponent fourier moments efms are pointed out an improvement of exponent fourier moments iefms is proposed the iefms avoid the imprecisions of efms and performs much better than efms

generalized vector version of minty s lemma and applications abstract in this paper we consider a generalized vector version of minty s lemma and then show the existence of solutions to generalized vector variational type inequality problems for set valued mappings as an application

random matrix theory and the zeros of ζ s we study the density of the roots of the derivative of the characteristic polynomial z u z of an n n random unitary matrix with distribution given by haar measure on the unitary group based on previous random matrix theory models of the riemann zeta function s this is expected to be an accurate description for the horizontal distribution of the zeros of s to the right of the critical line we show that as n the fraction of the roots of z u z that lie in the region 1 x n 1 z 1 tends to a limit function we derive asymptotic expressions for this function in the limits x and x 0 and compare them with numerical experiments

invariant character recognition with zernike and orthogonal fourier mellin moments abstract in this paper we consider the use of orthogonal moments for invariant classification of alphanumeric characters of different size in addition to the zernike and pseudo zernike moments zms and pzms which have been previously proposed for invariant character recognition a new method of combining orthogonal fourier mellin moments ofmms with centroid bounding circle scaling is introduced which is shown to be useful in characterizing images with large variability through extensive experimentation using zms and ofmms as features different scaling methodologies and classifiers it is shown that ofmms give the best overall performance in terms of both image reconstruction and classification accuracy

on mean values of mollifiers and l functions associated to primitive cusp forms we study the second moment of the l function associated to a holomorphic primitive cusp form of even weight perturbed by a new family of mollifiers this family is a natural extension of the mollifers considered by conrey and by bui conrey and young as an application we improve the current lower bound on critical zeros of holomorphic primitive cusp forms

generic orthogonal moments jacobi fourier moments for invariant image description a multi distorted invariant orthogonal moments jacobi fourier moments jfm were proposed the integral kernel of the moments was composed of radial jacobi polynomial and angular fourier complex componential factor the variation of two parameters in jacobi polynomial a and b can form various types of orthogonal moments legendre fourier moments a 1 b 1 chebyshev fourier moments a 2 b 32 orthogonal fourier mellin moments a 2 b 2 zernike moments and pseudo zernike moments and so on therefore jacobi fourier moments are generic expressions of orthogonal moments formed by a radial orthogonal polynomial and angular fourier complex component factor providing a common mathematical tool for performance analysis of the orthogonal moments in the paper jacobi fourier moments were calculated for a deterministic image and the original image was reconstructed with the moments the relationship between jacobi fourier moments and other orthogonal moments was studied theoretical analysis and experimental investigation were conducted in terms of the description performance and noise sensibility of the jfm

the distribution of the summatory function of the mobius function the summatory function of the mobius function is denoted m x in this article we deduce conditional results concerning m x assuming the riemann hypothesis and a conjecture of gonek and hejhal on the negative moments of the riemann zeta function assuming these conjectures we show that m x when appropriately normalized possesses a limiting distribution and also that a strong form of the weak mertens conjecture is true finally we speculate on the lower order of m x by studying the constructed distribution function

random matrices and l functions in recent years there has been a growing interest in connections between the statistical properties of number theoretical l functions and random matrix theory we review the history of these connections some of the major achievements and a number of applications

errata and comments on errata and comments on orthogonal moments based on exponent functions in this paper we demonstrate that improved exponent fourier moments mentioned in xiao et al 2015 1 are with crucial mistakes in its definition an image cannot be decomposed and reconstructed by these incorrect improved exponent fourier moments the corrected definition of improved exponent fourier moments is thus given in this paper to solve problems about numerical instability involved in the process of calculating the exponent fourier moments and values of radial functions approach infinity at origin experimental results show the superiority of the corrected improved exponent fourier moments highlightsmistakes are pointed out in xiao et al 1 corrected iefms are proposed as a response to xiao et al 1 experiments and theoretical analysis on corrected iefms

on the generalized vector variational inequality problem abstract in this paper we study vector variational inequalities with set valued mappings the concept of c x pseudomonotone mapping is introduced by employing the fan lemma we establish several existence results the new results extend and unify existence results of vector variational inequalities for single valued operators under the banach space setting

orthogonal moments based on exponent functions exponent fourier moments abstract in this paper we propose a new set of orthogonal moments based on exponent functions named exponent fourier moments efms which are suitable for image analysis and rotation invariant pattern recognition compared with zernike polynomials of the same degree the new radial functions have more zeros and these zeros are evenly distributed this property make efms have strong ability in describing image unlike zernike moments the kernel of computation of efms is extremely simple theoretical and experimental results show that exponent fourier moments perform very well in terms of image reconstruction capability and invariant recognition accuracy in noise free noisy and smooth distortion conditions the exponent fourier moments can be thought of as generalized orthogonal complex moments

explicit zero density estimate for the riemann zeta function near the critical line abstract in 1946 a selberg proved n t t 1 1 4 1 2 log t where n t is the number of nontrivial zeros of the riemann zeta function with and 0 t we provide an explicit version of this estimate together with an explicit approximate functional equation and an explicit upper bound for the second power moment of the zeta function on the critical line

the twisted mean square and critical zeros of dirichlet l functions in this work we obtain an asymptotic formula for the twisted mean square of a dirichlet l function with a longer mollifier whose coefficients are also more general than before as an application we obtain that for every dirichlet l function more than 41 72 of zeros are on the critical line and more than 40 74 of zeros are simple and on the critical line these proportions also improve previous results which were proved only for the riemann zeta function

zeros of combinations of the riemann ξ function and the confluent hypergeometric function on bounded vertical shifts abstract in 1914 hardy proved that infinitely many non trivial zeros of the riemann zeta function lie on the critical line using the transformation formula of the jacobi theta function recently the first author obtained an integral representation involving the riemann function and the confluent hypergeometric function linked to the general theta transformation using this result we show that a series consisting of bounded vertical shifts of a product of the riemann function and the real part of a confluent hypergeometric function has infinitely many zeros on the critical line thereby generalizing a previous result due to the first and the last authors along with roy and robles the latter itself is a generalization of hardy s theorem

on the solution semicontinuity to a parametric generalized vector quasivariational inequality in this paper the semicontinuities of the solution set map are investigated for a parametric generalized vector quasivariational inequality in locally convex hausdorff topological vector spaces the upper semicontinuity and closedness of the solution set map are obtained a parametric gap function is proposed by using a nonlinear scalarization function by virtue of the parametric gap function and a key assumption the hausdorff lower semicontinuity of the solution set map is established

the twisted fourth moment of the riemann zeta function we compute the asymptotics of the fourth moment of the riemann zeta func tion times an arbitrary dirichlet polynomial of length t 1 11 the study of the moments of the riemann zeta function has a long and distinguished history starting with the work of hardy and littlewood in 1918 and continuing to the present day one motivation for understanding moments is that they yield information about the maximum size of the zeta function the lindelof hypothesis another application is to zero density estimates which in turn have consequences for primes in short intervals however they have become an interesting topic in their own right very few rigorous results are known just the second and fourth power moments indeed it is only recently that a believable conjecture for higher powers has been made the twisted moments that is moments of the riemann zeta function times an arbitrary dirichlet polynomial are important too for example levinson s method of detecting zeros of the zeta function lying on the critical line requires knowing the asymptotics of the mollified second moment in a series of papers duke friedlander and iwaniec used estimates for amplified moments of a family of l functions in order to deduce a subconvexity bound for an individual member of the family of course there are far easier methods to give a subconvexity bound for zeta but there are close analogies between different families and it is desirable to understand the structure of these amplified moments in general in this paper we prove an asymptotic formula for the twisted fourth moment of the riemann zeta function where we may take a dirichlet polynomial of length up to t 1 11 e

ramanujan hardy littlewood riesz phenomena for hecke forms abstract we generalize a result of ramanujan hardy and littlewood to the setting of primitive hecke forms which interestingly exhibits faster convergence than in the initial case of the riemann zeta function we also provide a criterion in the spirit of riesz for the riemann hypothesis for the associated l functions