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pro vyhledávání: '"11M06"'
Conrey and Ghosh studied the second moment of the Riemann zeta function, evaluated at its local extrema along the critical line, finding the leading order behaviour to be $\frac{e^2 - 5}{2 \pi} T (\log T)^2$. This problem is closely related to a mixe
Externí odkaz:
http://arxiv.org/abs/2411.05573
Autor:
Pearce-Crump, Andrew
Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non-trivial zeros of the zeta function, resolving a problem known as Shanks' conjecture. Conrey and Ghosh studied the second moment of th
Externí odkaz:
http://arxiv.org/abs/2411.05568
Autor:
Quesada-Herrera, Emily
We give an exposition of some connections between Fourier optimization problems and problems in number theory. In particular, we present some recent conditional bounds under the generalized Riemann hypothesis, achieved via a Fourier optimization fram
Externí odkaz:
http://arxiv.org/abs/2411.05095
Autor:
Gao, Peng, Zhao, Liangyi
We establish sharp lower bounds for shifted moments of Dirichlet $L$-function of fixed modulus under the generalized Riemann hypothesis.
Externí odkaz:
http://arxiv.org/abs/2411.03692
Conditional upper and lower bounds for $L$-functions in the Selberg class close to the critical line
Autor:
Palojärvi, Neea, Simonič, Aleksander
Assuming the Generalized Riemann Hypothesis, we provide uniform upper and lower bounds with explicit main terms for $\log{\left|\mathcal{L}(s)\right|}$ for $\sigma \in (1/2,1)$ and for functions in the Selberg class. We also provide estimates under a
Externí odkaz:
http://arxiv.org/abs/2410.22711
Autor:
Hosoi, Manami, Umegaki, Yumiko
Let $\chi$ be a primitive Dirichlet character whose conductor $q$ is a prime number. For the certain averages of values of $\log |L(s, \chi)|$ in $q$-aspect at a fixed $s=\sigma>1/2$, under Generalized Riemann Hypothesis (GRH), we explain it can be w
Externí odkaz:
http://arxiv.org/abs/2410.20341
Autor:
Endo, Kenta
In 1979, Gonek presented the hybrid joint universality theorem for Dirichlet $L$-functions and proved the universality theorem for Hurwitz zeta-functions with rational parameter as an application. Following the introduction of the hybrid universality
Externí odkaz:
http://arxiv.org/abs/2410.17575
Autor:
Gupta, Rajat, Savalia, Aditi
Publikováno v:
Journal of Number Theory, Volume 265, December 2024, Pages 270-290
In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function $\sigma_{\alpha}(n):=\sum_{d|n}d^{\alpha}$. We obtain an exact identity relating the Dirichlet series $\zeta(s)\zet
Externí odkaz:
http://arxiv.org/abs/2410.16940
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:
Kanungo, Shihan, Schettler, Jordan
In this note, we evaluate a multivariable family of infinite products which generalize Guillera's infinite product for $e$, and Ser's formula (rediscovered by Sondow) for $e^\gamma$. We describe formulas for the products in terms of special values of
Externí odkaz:
http://arxiv.org/abs/2410.07534