Zobrazeno 1 - 10
of 253
pro vyhledávání: '"Goldston D"'
Autor:
Goldston, D. A., Suriajaya, Ade Irma
Publikováno v:
Res. Number Theory 8 (2022), article number: 71
We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery's conjecture for the pair correlation of zeros of the Riemann zeta-function which are uniform in lo
Externí odkaz:
http://arxiv.org/abs/2205.06503
Autor:
Goldston, D. A., Suriajaya, Ade Irma
Publikováno v:
Nagoya Math. J. 250 (2023), 511-532
Fujii obtained a formula for the average number of Goldbach representations with lower order terms expressed as a sum over the zeros of the Riemann zeta-function and a smaller error term. This assumed the Riemann Hypothesis. We obtain an unconditiona
Externí odkaz:
http://arxiv.org/abs/2110.14250
Autor:
Goldston, D. A., Suriajaya, Ade Irma
We generalize the work of Fei, Bhowmik and Halupczok, and Jia relating the Goldbach conjecture to real zeros of Dirichlet $L$-functions.
Externí odkaz:
http://arxiv.org/abs/2104.09407
Autor:
Goldston, D. A., Suriajaya, Ade Irma
Publikováno v:
Acta Arith. 200 (2021), 71-90
We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta
Externí odkaz:
http://arxiv.org/abs/2007.16099
Autor:
Goldston, D. A., Suriajaya, Ade Irma
Publikováno v:
J. Number Theory 227 (2021), 144-157
We show that the error term in the asymptotic formula for the Ces{\`a}ro mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures cannot be too small and oscillates.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2007.14616
Assuming the Riemann Hypothesis, we improve on previous results by proving there are infinitely many zeros of the Riemann zeta-function whose differences are smaller than 0.50412 times the average spacing. To obtain this result, we generalize a set o
Externí odkaz:
http://arxiv.org/abs/1904.06001
Autor:
Goldston, D. A., Pandey, M.
In this paper, we obtain bounds on the $L^1$ norm of the sum $\sum_{n\le x}\tau(n) e(\alpha n)$ where $\tau(n)$ is the divisor function.
Externí odkaz:
http://arxiv.org/abs/1704.05953
A Prime Difference Champion (PDC) for primes up to $x$ is defined to be any element of the set of one or more differences that occur most frequently among all positive differences between primes $\le x$. Assuming an appropriate form of the Hardy-Litt
Externí odkaz:
http://arxiv.org/abs/1612.02938
Autor:
Goldston, D. A., Yang, Liyang
Assuming the Riemann Hypothesis, we obtain asymptotic formulas for the average number representations of an even integer as the sum of two primes. We use the method of Bhowmik and Schlage-Puchta and refine their results slightly to obtain a more rece
Externí odkaz:
http://arxiv.org/abs/1601.06902
We obtain an asymptotic formula for a weighted sum of the square of the tail of the singular series for the Goldbach and prime-pair problems.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/1409.2151