Zobrazeno 1 - 10
of 80
pro vyhledávání: '"Hiary, Ghaith A."'
Riemann numerically approximated at least three zeta zeros. According to Edwards, Riemann even took steps to verify that the lowest zero he computed was indeed the first zeta zero. This approach to verification is developed, improved, and generalized
Externí odkaz:
http://arxiv.org/abs/2408.00187
Explicit estimates for the Riemann zeta-function on the $1$-line are derived using various methods, in particular van der Corput lemmas of high order and a theorem of Borel and Carath\'{e}odory.
Comment: 31 pages
Comment: 31 pages
Externí odkaz:
http://arxiv.org/abs/2306.13289
Autor:
Hales, Jonathon, Hiary, Ghaith
A new deterministic algorithm for finding square divisors, and finding $r$-power divisors in general, is presented. This algorithm is based on Lehman's method for integer factorization and is straightforward to implement. While the theoretical comple
Externí odkaz:
http://arxiv.org/abs/2209.15586
Autor:
Hiary, Ghaith, Paasche, Megan
An interesting episode in the history of the prime number theorem concerns a formula proposed by Legendre for counting the primes below a given bound. We point out that arithmetic bias likely played an important role in arriving at that formula and i
Externí odkaz:
http://arxiv.org/abs/2208.02623
Autor:
Akula, Aditya, Hiary, Ghaith
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.
Comment: 13 page
Comment: 13 page
Externí odkaz:
http://arxiv.org/abs/2207.06552
An explicit subconvex bound for the Riemann zeta function $\zeta(s)$ on the critical line $s=1/2+it$ is proved. Previous subconvex bounds relied on an incorrect version of the Kusmin-Landau lemma. After accounting for the needed correction in that le
Externí odkaz:
http://arxiv.org/abs/2207.02366
Publikováno v:
In Journal of Number Theory March 2024 256:195-217
Akademický článek
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Autor:
Hiary, Ghaith, Vandehey, Joseph
We study the density of the invariant measure of the Hurwitz complex continued fraction from a computational perspective. It is known that this density is piece-wise real-analytic and so we provide a method for calculating the Taylor coefficients aro
Externí odkaz:
http://arxiv.org/abs/1805.10151
Autor:
Hiary, Ghaith A.
Several asymptotic expansions and formulas for cubic exponential sums are derived. The expansions are most useful when the cubic coefficient is in a restricted range. This generalizes previous results in the quadratic case and helps to clarify how to
Externí odkaz:
http://arxiv.org/abs/1707.03448