Zobrazeno 1 - 10
of 86
pro vyhledávání: '"Milinovich, Micah B."'
By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of estimating the
Externí odkaz:
http://arxiv.org/abs/2404.08380
Inspired by a result of Soundararajan, assuming the Riemann hypothesis (RH), we prove a new inequality for the logarithm of the modulus of the Riemann zeta-function on the critical line in terms of a Dirichlet polynomial over primes and prime powers.
Externí odkaz:
http://arxiv.org/abs/2403.17803
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
Assuming the Riemann hypothesis, we improve the current upper and lower bounds for the average value of Montgomery's function $F(\alpha, T)$ over long intervals by means of a Fourier optimization framework. The function $F(\alpha, T)$ is often used t
Externí odkaz:
http://arxiv.org/abs/2310.01913
Assuming the Riemann hypothesis, we prove estimates for the variance of the real and imaginary part of the logarithm of the Riemann zeta-function in short intervals. We give three different formulations of these results. Assuming a conjecture of Chan
Externí odkaz:
http://arxiv.org/abs/2211.14918
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
Generalizing previous work of Iwaniec, Luo, and Sarnak (2000), we use information from one-level density theorems to estimate the proportion of non-vanishing of $L$-functions in a family at a low-lying height on the critical line (measured by the ana
Externí odkaz:
http://arxiv.org/abs/2109.10844
We study three integrals related to the celebrated pair correlation conjecture of H. L. Montgomery. The first is the integral of Montgomery's function $F(\alpha, T)$ in bounded intervals, the second is an integral introduced by Selberg related to est
Externí odkaz:
http://arxiv.org/abs/2108.09258
Autor:
Carneiro, Emanuel, Das, Mithun Kumar, Florea, Alexandra, Kumchev, Angel V., Malik, Amita, Milinovich, Micah B., Turnage-Butterbaugh, Caroline, Wang, Jiuya
Publikováno v:
J. Funct. Anal. 281 (2021), no. 9, Paper No. 109199
We improve the current bounds for an inequality of Erd\H{o}s and Tur\'an from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upon a recent work of Soundararajan, we establish a novel connectio
Externí odkaz:
http://arxiv.org/abs/2104.00105
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