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of 87
pro vyhledávání: '"Li, Xiannan"'
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
Autor:
Li, Xiannan
We prove an asymptotic for the second moment of quadratic twists of a modular $L$-function. This was previously known conditionally on GRH by the work of Soundararajan and Young.
Comment: 32 pgs. Minor revisions
Comment: 32 pgs. Minor revisions
Externí odkaz:
http://arxiv.org/abs/2208.07343
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:
Zhang, Xiaolei, Tian, Jiangping, Li, Xiannan, Yin, Shuo, Cui, Zechuan, Yang, Hongen, Zhou, Qingxing
Publikováno v:
In Applied Thermal Engineering 1 October 2024 254
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
Autor:
Li, Xiannan
A distinguishing feature of certain intractable problems in prime number theory is the sparsity of the underlying sequence. Motivated by the general problem of finding primes in sparse polynomial sequences, we give an estimate for the number of prime
Externí odkaz:
http://arxiv.org/abs/2111.05403
Akademický článek
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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