Related papers: Two dimensional value-distribution of cubic Hecke …

In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian, and various spaces of delta-functions including…

In this paper, Wang's log-Harnack inequality and exponential ergodicity are derived for two types of distribution dependent SDEs: one is the CKLS model, where the diffusion coefficient is a power function of order $\theta$ with…

Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.

In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.

We study some problems on the distribution of values of symmetric power $L$-functions at $s=1$ in both aspects of level and weight: bounds of these values, extreme values, Montgomery-Vaughan's conjecture and distribution functions. Our…

In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight $w(x){\rm d}x = \log \frac{2k}{1-x}{\rm d}x$ on $(-1,1)$, $k > 1$, and verify a conjecture of…

$L-$series attached to two classical families of elliptic curves with complex multiplications are studied over number fields, formulae for their special values at $s=1, $ bound of the values, and criterion of reaching the bound are given.…

Let H be a split reductive group over a local non-archimedean field, and let H^ denote its Langlands dual group. We present an explicit formula for the generating function of an unramified L-function associated to a highest weight…

This paper aims to explore the quasiasymptotic behavior of distributions through the fractional Hankel transform. We present Tauberian result that connects the asymptotic behavior of generalized functions in the Zemanian space with the…

Let $\lambda$ be a self-dual Hecke character over a CM field $K$. Let $\mathfrak{p}$ be a degree one prime of the maximal totally real subfield $F$ of $K$ and $\Gamma_{\mathfrak{p}}$ the Galois group of the anticyclotomic…

The conjectures of Deligne, Be\u\i linson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their $L$-functions. We make a numerical study for symmetric power…

Motivated by applications to the study of L-functions, we develop an asymptotic version of the large sieve inequality for linear forms in primitive Dirichlet characters.

Let $\chi$ be a Dirichlet character modulo $q$, let $L(s, \chi)$ be the attached Dirichlet $L$-function, and let $L^\prime(s, \chi)$ denotes its derivative with respect to the complex variable $s$. The main purpose of this paper is to give…

We study the value-distribution of the Hurwitz zeta-function with algebraic irrational parameter $\zeta(s;\alpha)=\sum_{n\geq_0}(n+\alpha)^{-s}$. In particular, we prove effective denseness results of the Hurwitz zeta-function and its…

For $\chi_k$ a self$-$dual primitive Dirichlet character mod $k$ several reduced identities of Dirichlet $L-$functions $L_k(s):=L(s,\chi_k)$, expressed as linear combinations of Hurwitz $\zeta$ functions, are found for $s=2,3$ and some…

We study the first moments of central values of Hecke $L$-functions associated with quadratic, cubic and quartic symbols to prime moduli. This also enables us to obtain results on first moments of central values of certain families of cubic…

We derive the probability distribution of product of two independent random variables, each distributed according the one-dimensional stable law. We represent the density by its power series and its asymptotic expansions. As Fox's…

We give a new proof of Heath-Brown's full asymptotic expansion for the second moment of Dirichlet L-functions and we obtain a corresponding asymptotic expansion for a twisted first moment of Hecke-Maass L-functions.

Let $-D < -4$ denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of $\Bbb Q(\sqrt{-D})$ exists. Let $d$ be a fundamental discriminant prime to $D$. Let $2k-1$ be an odd natural…

Assuming the generalized Riemann hypothesis and a bound for the negative discrete moments of the Riemann zeta function (resp. Dirichlet $L$-functions), we prove the existence of a logarithmic limiting distribution for the normalized partial…