Zobrazeno 1 - 10
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pro vyhledávání: '"Hung M., P."'
We obtain conditional upper bounds for negative discrete moments of the derivative of the Riemann zeta-function averaged over a subfamily of zeros of the zeta function which is expected to have full density inside the set of all zeros. For $k\leq 1/2
Externí odkaz:
http://arxiv.org/abs/2310.03949
We study a class of nonconvex nonsmooth optimization problems in which the objective is a sum of two functions: One function is the average of a large number of differentiable functions, while the other function is proper, lower semicontinuous and ha
Externí odkaz:
http://arxiv.org/abs/2305.06848
Autor:
Bui, Hung M., Hall, R. R.
Using the twisted fourth moment of the Riemann zeta-function we study large gaps between consecutive zeros of the derivatives of Hardy's function $Z(t)$, improving upon previous results of Conrey and Ghosh [J. London Math. Soc. 32 (1985), 193--202],
Externí odkaz:
http://arxiv.org/abs/2304.05181
Autor:
Bui, Hung M., Hall, R. R.
Let $Z^{(k)}(t)$ be the $k$-th derivative of Hardy's $Z$-function. The numerics seem to suggest that if $k$ and $\ell$ have the same parity, then the zeros of $Z^{(k)}(t)$ and $Z^{(\ell)}(t)$ come in pairs which are very close to each other. That is
Externí odkaz:
http://arxiv.org/abs/2304.05178
Autor:
Hung M. Vu, Ju Yeon Lee, Yongmin Kim, Sanghoon Park, Fabiana Izaguirre, Juhyeon Lee, Jung-Hyun Lee, Minjoung Jo, Hye Ryun Woo, Jin Young Kim, Pyung Ok Lim, Min-Sik Kim
Publikováno v:
Journal of Analytical Science and Technology, Vol 15, Iss 1, Pp 1-10 (2024)
Abstract Background Recent advances in high-resolution mass spectrometry have now enabled the study of proteomes at the single-cell level, offering the potential to unveil novel aspects of cellular processes. Remarkably, there has been no prior attem
Externí odkaz:
https://doaj.org/article/029d13a4f7294960b9c29f862c5583fd
Autor:
Bui, Hung M., Florea, Alexandra
Assuming the Riemann Hypothesis we study negative moments of the Riemann zeta-function and obtain asymptotic formulas in certain ranges of the shift in $\zeta(s)$. For example, integrating $|\zeta(1/2+\alpha+it)|^{-2k}$ with respect to $t$ from $T$ t
Externí odkaz:
http://arxiv.org/abs/2302.07226
Erd\H{o}s, Graham, and Selfridge considered, for each positive integer $n$, the least value of $t_n$ so that the integers $n+1, n+2, \dots, n+t_n $ contain a subset the product of whose members with $n$ is a square. An open problem posed by Granville
Externí odkaz:
http://arxiv.org/abs/2211.12467
We show assuming RH that phenomena concerning pairs of zeros established $via$ pair correlations occur with positive density (with at most a slight adjustment of the constants). Also, while a double zero is commonly considered to be a close pair, we
Externí odkaz:
http://arxiv.org/abs/2208.02359
Let $P$ be a polynomial with integer coefficients and degree at least two. We prove an upper bound on the number of integer solutions $n\leq N$ to $n! = P(x)$ which yields a power saving over the trivial bound. In particular, this applies to a centur
Externí odkaz:
http://arxiv.org/abs/2204.08423
We prove special cases of the Ratios Conjecture for the family of quadratic Dirichlet $L$--functions over function fields. More specifically, we study the average of $L(1/2+\alpha,\chi_D)/L(1/2+\beta,\chi_D)$, when $D$ varies over monic, square-free
Externí odkaz:
http://arxiv.org/abs/2109.10396