4 citations · 10 across the 10 of their papers we have counts for
10 papers
On the asymptotic duality of spectral variances in random matrix theory and the "1/6" formula
Peng Tian, Roman Riser, Eugene Kanzieper
A "mysterious" relation between the number variance and the variance of the -th ordered eigenvalue, first suggested by French et al. [Ann. Phys. 113, 277 (1978)], is revisited a…
Statistics of local level spacings in single- and many-body quantum chaos
Peng Tian, Roman Riser, Eugene Kanzieper
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine…
The size function for imaginary cyclic sextic fields
Ha Thanh Nguyen Tran, Peng Tian, Amy Feaver
In this paper, we investigate the size function for number fields. This size function is analogous to the dimension of the Riemann-Roch spaces of divisors on an algebraic cur…
Ratio-consistent estimation for long range dependent Toeplitz covariance with application to matrix data whitening
Peng Tian, Jianfeng Yao
We consider a data matrix from a multivariate stationary process with a separable covariance function, where is a positive semi-definite…
Joint CLT for top eigenvalues of sample covariance matrices of separable high dimensional long memory processes
Peng Tian
For , consider the sample covariance matrix from a data set , where is a matrix having…
Realization of Modular Galois Representations in Jacobians of modular curves
Peng Tian
In this paper, we propose an improved algorithm for computing mod Galois representations associated to eigenforms of arbitrary levels prime to . Precisely, we present…
Computing modular Galois representations for small
Peng Tian
In this paper we describe an algorithm for computing mod Galois representations associated to modular forms of weight when . As applications, we use this algo…
The size function for cyclic cubic fields
Ha Thanh Nguyen Tran, Peng Tian
The size function for a number field is an analogue of the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. It was conjectured to attain its maximum at the t…
Non-vanishing Fourier coefficients of modular forms
Peng Tian, Hourong Qin
In this paper, we generalize D. H. Lehmer's result to give a sufficient condition for level one cusp forms with integral Fourier coefficients such that the smallest for whi…
Computations of Galois Representations Associated to Modular Forms
Peng Tian
We propose an improved algorithm for computing mod Galois representations associated to a cusp form of level one. The proposed method allows us to explicitly compute the…