Zobrazeno 1 - 10
of 89
pro vyhledávání: '"Chandee, Vorrapan"'
In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$-functions at the central point, averaged over primitive characters $\chi$ modulo $q$ and all moduli $q \leq Q$. In 2007, as an application of their ``asymptotic large
Externí odkaz:
http://arxiv.org/abs/2409.01457
We study a new orthogonal family of $L$-functions associated with holomorphic Hecke newforms of level $q$, averaged over $q \asymp Q$. To illustrate our methods, we prove a one level density result for this family with the support of the Fourier tran
Externí odkaz:
http://arxiv.org/abs/2310.07606
We prove an asymptotic formula for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line. Previously the same result was shown condit
Externí odkaz:
http://arxiv.org/abs/2307.13194
We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the $k$-divisor functions, where $k \neq 10^j$, and Hecke eigenvalues of newforms, such as Ramanujan tau function, are
Externí odkaz:
http://arxiv.org/abs/2203.13117
Autor:
Chandee, Vorrapan, Li, Xiannan
Publikováno v:
Adv. Math. 365 (2020)
In this paper, we obtain upper bounds for the second moment of $L(u_j \times \phi, \frac{1}{2} + it_j)$, where $\phi$ is a Hecke Maass form for $SL(4, \mathbb Z)$, and $u_j$ is taken from an orthonormal basis of Hecke-Maass forms on $SL(2, \mathbb{Z}
Externí odkaz:
http://arxiv.org/abs/2111.05406
We study three integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. The first is the integral of Montgomery's function $F(\alpha, T)$ in bounded intervals, the second is an integral introduced by Selberg related to est
Externí odkaz:
http://arxiv.org/abs/2108.09258
Autor:
Chandee, Vorrapan, Li, Xiannan
We prove a Lindel\"of on average bound for the eighth moment of a family of $L$-functions attached to automorphic forms on $GL(2)$, the first time this has been accomplished. Previously, such a bound had been proven for the sixth moment for our famil
Externí odkaz:
http://arxiv.org/abs/1708.08410
Autor:
Chandee, Vorrapan, Li, Xiannan
Publikováno v:
Algebra and Number Theory (2017) 11 (3), 583-633
In this paper, we consider the $L$-functions $L(s, f)$ where $f$ is an eigenform for the congruence subgroup $\Gamma_1(q)$. We prove an asymptotic formula for the sixth moment of this family of automorphic $L$-functions.
Externí odkaz:
http://arxiv.org/abs/1708.08406
Autor:
Chandee, Vorrapan, Lee, Yoonbok
Katz and Sarnak conjectured that the statistics of low-lying zeros of various family of $L$-functions matched with the scaling limit of eigenvalues from the random matrix theory. In this paper we confirm this statistic for a family of primitive Diric
Externí odkaz:
http://arxiv.org/abs/1706.02848
Publikováno v:
Mathematische Zeitschrift, vol. 281 (2015), 315-332
Let $\pi S(t)$ denote the argument of the Riemann zeta-function at the point $s=\tfrac12+it$. Assuming the Riemann hypothesis, we give a new and simple proof of the sharpest known bound for $S(t)$. We discuss a generalization of this bound for a larg
Externí odkaz:
http://arxiv.org/abs/1503.00955