Zobrazeno 1 - 10
of 1 922
pro vyhledávání: '"11M26"'
Autor:
Blomer, Valentin, Thorner, Jesse
We combine the relative trace formula with analytic methods to obtain zero density estimate for $L$-functions in various families of automorphic representations for $\mathrm{GL}(m)$. Applications include strong bounds for the average analytic rank of
Externí odkaz:
http://arxiv.org/abs/2410.17158
Autor:
Banks, William D.
For a primitive Dirichlet character $X$, a new hypothesis $RH_{sim}^\dagger[X]$ is introduced, which asserts that (1) all simple zeros of $L(s,X)$ in the critical strip are located on the critical line, and (2) these zeros satisfy some specific condi
Externí odkaz:
http://arxiv.org/abs/2410.11605
Autor:
Corrigan, C. C.
In this article, we establish a large sieve inequality for additive characters to moduli in the range of appropriate integer polynomials of degree two. As an application, we derive a weighted zero-density estimate for twists of $L$-functions associat
Externí odkaz:
http://arxiv.org/abs/2410.05704
Autor:
Charge, Shashank, Dixit, Atul
We derive Vorono\"{\dotlessi} summation formulas for the Liouville function $\lambda(n)$, the M\"{o}bius function $\mu(n)$, and for $d^{2}(n)$, where $d(n)$ is the divisor function. The formula for $\lambda(n)$ requires explicit evaluation of certain
Externí odkaz:
http://arxiv.org/abs/2410.04506
Autor:
Crider, Sarah M., Hillstrom, Shawn
An incomplete Riemann zeta function can be expressed as a lower-bounded, improper Riemann-Liouville fractional integral, which, when evaluated at $0$, is equivalent to the complete Riemann zeta function. Solutions to Landau's problem with $\zeta(s) =
Externí odkaz:
http://arxiv.org/abs/2410.01069
Autor:
Garg, Meghali, Maji, Bibekananda
In 1916, Riesz gave an equivalent criterion for the Riemann hypothesis (RH). Inspired from Riesz's criterion, Hardy and Littlewood showed that RH is equivalent to the following bound: \begin{align*} P_1(x):= \sum_{n=1}^\infty \frac{\mu(n)}{n} \exp\le
Externí odkaz:
http://arxiv.org/abs/2409.17708
Autor:
Broucke, Frederik
We show the zero-density estimate \[ N(\zeta_{\mathcal{P}}; \alpha, T) \ll T^{\frac{4(1-\alpha)}{3-2\alpha-\theta}}(\log T)^{9} \] for Beurling zeta functions $\zeta_{\mathcal{P}}$ attached to Beurling generalized number systems with integers distrib
Externí odkaz:
http://arxiv.org/abs/2409.10051
Autor:
Chavez, Gordon
We show that under the Riemann hypothesis and simplicity of the nontrivial zeros $\rho_{n}$ of the zeta function $\zeta(s)$ $$ \frac{1}{\zeta(1+\alpha)}\int_{1}^{\infty}\frac{M^{2}(u)}{u^{2+\alpha}}du \biggr\vert_{\alpha=0} \leq \frac{3}{\pi^{2}} $$
Externí odkaz:
http://arxiv.org/abs/2409.02106
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
Autor:
Matsumoto, Kohji, Suzuki, Masatoshi
We study the $M$-functions, which describe the limit theorem for the value-distributions of the secondary main terms in the asymptotic formulas for the summatory functions of the Goldbach counting function. One of the new aspects is a sufficient cond
Externí odkaz:
http://arxiv.org/abs/2409.00888