Zobrazeno 1 - 10
of 31
pro vyhledávání: '"11M06, 11M50"'
Autor:
Shen, Quanli, Stucky, Joshua
We prove an asymptotic formula with four main terms for the fourth moment of quadratic Dirichlet $L$-functions unconditionally. Our proof is based on the work of Li , Soundararajan, and Soundararajan-Young. Our proof requires several new ingredients.
Externí odkaz:
http://arxiv.org/abs/2402.01497
Autor:
Darses, Sébastien, Najnudel, Joseph
We prove exact formulas for weighted $2k$th moments of the Riemann zeta function for all integer $k\geq 1$ in terms of the analytic continuation of an auto-correlation function. This latter enjoys several functional equations. One of them, following
Externí odkaz:
http://arxiv.org/abs/2311.02783
We prove a lower bound on the maximum of the Riemann zeta function in a typical short interval on the critical line. Together with the upper bound from the previous work of the authors, this implies tightness of $$ \max_{|h|\leq 1}|\zeta(\tfrac 12+{\
Externí odkaz:
http://arxiv.org/abs/2307.00982
Autor:
Arguin, Louis-Pierre, Bailey, Emma
For $V\sim \alpha \log\log T$ with $0<\alpha<2$, we prove \[ \frac{1}{T}\text{meas}\{t\in [T,2T]: \log|\zeta(1/2+ {\rm i} t)|>V\}\ll \frac{1}{\sqrt{\log\log T}} e^{-V^2/\log\log T}. \] This improves prior results of Soundararajan and of Harper on the
Externí odkaz:
http://arxiv.org/abs/2202.06799
Selberg's central limit theorem states that the values of $\log|\zeta(1/2+i \tau)|$, where $\tau$ is a uniform random variable on $[T,2T]$, is distributed like a Gaussian random variable of mean $0$ and standard deviation $\sqrt{\frac{1}{2}\log \log
Externí odkaz:
http://arxiv.org/abs/2104.07403
Autor:
Bettin, Sandro, Conrey, J. Brian
We consider the asymptotic behavior of the mean square of truncations of the Dirichlet series of $\zeta(s)^k$. We discuss the connections of this problem with that of the variance of the divisor function in short intervals and in arithmetic progressi
Externí odkaz:
http://arxiv.org/abs/2002.09466
Autor:
Shen, Quanli
We study the fourth moment of quadratic Dirichlet $L$-functions at $s= \frac{1}{2}$. We show an asymptotic formula under the generalized Riemann hypothesis, and obtain a precise lower bound unconditionally. The proofs of these results follow closely
Externí odkaz:
http://arxiv.org/abs/1907.01107
Autor:
Conrey, Brian, Keating, Jonathan P.
In this series of papers we examine the calculation of the $2k$th moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes the general study of
Externí odkaz:
http://arxiv.org/abs/1701.06651
Autor:
Najnudel, Joseph
In the present paper, we show that under the Riemann hypothesis, and for fixed $h, \epsilon > 0$, the supremum of the real and the imaginary parts of $\log \zeta (1/2 + it)$ for $t \in [UT -h, UT + h]$ are in the interval $[(1-\epsilon) \log \log T,
Externí odkaz:
http://arxiv.org/abs/1611.05562
Autor:
Bourgade, Paul, Kuan, Jeffrey
Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions towards a Gaussian field, with covariance structure corresponding to the $\HH^{1/2}$-norm of the test functions. For this purpose, we obta
Externí odkaz:
http://arxiv.org/abs/1203.5328