Random matrix theory and moments of moments of L-functions
نویسندگان
چکیده
In this paper, we give an analytic proof of the asymptotic behavior moments characteristic polynomials random symplectic and orthogonal matrices. We therefore obtain alternate, integral expressions for leading order coefficients previously found by Assiotis, Bailey Keating. also discuss conjectures Keating corresponding [Formula: see text]-functions with symmetry. Specifically, show that these follow from shifted conjecture Conrey, Farmer, Keating, Rubinstein Snaith.
منابع مشابه
SOME RESULTS OF MOMENTS OF UNCERTAIN RANDOM VARIABLES
Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable...
متن کاملIntegral Moments of L-functions
We give a new heuristic for all of the main terms in the integral moments of various families of primitive L-functions. The results agree with previous conjectures for the leading order terms. Our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary, orthogonal, or symplectic matrices, where the mom...
متن کاملMatrix Computation and the Theory of Moments∗
We study methods to obtain bounds or approximations to u f(A)v where A is a symmetric, positive definite matrix and f is a smooth function. These methods are based on the use of quadrature rules and the Lanczos algorithm. We give some theoretical results on the behavior of these methods based on results for orthogonal polynomials as well as analytical bounds and numerical experiments on a set o...
متن کاملMatrix measures, random moments and Gaussian ensembles
We consider the moment space Mn corresponding to p × p real or complex matrix measures defined on the interval [0, 1]. The asymptotic properties of the first k components of a uniformly distributed vector (S1,n, . . . , Sn,n) ∗ ∼ U(Mn) are studied if n → ∞. In particular, it is shown that an appropriately centered and standardized version of the vector (S1,n, . . . , Sk,n) ∗ converges weakly to...
متن کاملLower bounds for moments of L-functions.
The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith [(2000) Commun. Math. Phys. 214, 57-89 and 91-110], there are now precise conjectures for their limiting values. We develop a simple method to establish lower bounds of the conjectured order of magnitude for several such families of L-functions. As an example ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Random matrices : theory and applications
سال: 2022
ISSN: ['2010-3263', '2010-3271']
DOI: https://doi.org/10.1142/s2010326323500028