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Keith Billington, Maddie Cheng, Jordan Schettler, Ade Irma Suriajaya, The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function, In this paper, we prove an unconditional form of Fujii's formula for the average number of Goldbach representations and show that the error in this formula is determined by a general zero-free region of the Riemann zeta-function, and vice versa. In particular, we describe the error in the unconditional formula in terms of the remainder in the Prime Number Theorem which connects the error to zero-free regions of the Riemann zeta-function.. |
2. |
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya, Caroline L. Turnage-Butterbaugh, An Unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function, Acta Arith., 10.4064/aa230612-20-3, Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least 67.9% of the nontrivial zeros are simple. Here we obtain an unconditional form of Montgomery's theorem and show how to apply it to prove the following result on simple zeros: Assuming all the zeros ρ=β+iγ of the Riemann zeta-function such that T^{3/8} |
3. |
Jörn Steuding, Ade Irma Suriajaya, Mean-Values Associated with Generalized Schemmel's Function, Ann. Univ. Sci. Budapest. Sect. Comput., 54, 307-319, 2023.09. |
4. |
Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya, The a-points of the Riemann zeta-function and the functional equation, In: Number Theory in Memory of Eduard Wirsing (2023), H. Maier et al. (eds.), Springer Nature Switzerland AG, 10.1007/978-3-031-31617-3_21, 21, 307-321, 2023.08. |
5. |
Daniel A. Goldston, Ade Irma Suriajaya, On a smoothed average of the number of Goldbach representations, In: Number Theory in Memory of Eduard Wirsing (2023), H. Maier et al. (eds.), Springer Nature Switzerland AG, 10.1007/978-3-031-31617-3_10, 10, 145-156, 2023.04. |
6. |
Sneha Chaubey, Suraj Singh Khurana, Ade Irma Suriajaya, Zeros of derivatives of L-functions in the Selberg class on Re(s)Proc. Amer. Math. Soc., 10.1090/proc/16251, 151, 1855-1866, 2023.02. ![](/images/qirlink_f_20140718.gif) |
7. |
Daniel A. Goldston, Ade Irma Suriajaya, On an Average Goldbach Representation Formula of Fujii, Nagoya Math. J., 10.1017/nmj.2022.44, 250, 511-532, 2023.01. |
8. |
Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya, Riemann-Type Functional Equations -- Julia Line and Counting Formulae --, Indag. Math., 10.1016/j.indag.2022.08.002, 33, 6, 1236-1262, 2022.11. |
9. |
Daniel A. Goldston, Ade Irma Suriajaya, The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function, Res. Number Theory, 10.1007/s40993-022-00371-4, 8, 71, 2022.09. |
10. |
Shingo Sugiyama, Ade Irma Suriajaya, Weighted one-level density of low-lying zeros of Dirichlet L-functions, Res. Number Theory, 10.1007/s40993-022-00359-0, 8, 55, 2022.08. |
11. |
Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya, Riemann-Type Functional Equations -- Dirichlet Polynomial Approximations and a Weak Gram Law --, Acta Arith., 10.4064/aa210111-13-4, 204, 97-113, 2022.06. |
12. |
John B. Friedlander, Daniel A. Goldston, Henryk Iwaniec, Ade Irma Suriajaya, Exceptional zeros and the Goldbach problem, J. Number Theory, 10.1016/j.jnt.2021.06.004, 233, 78-86, 2022.04, We show that the assumption of a weak form of the Hardy-Littlewood conjecture on the Goldbach problem suffices to disprove the possible existence of exceptional zeros of Dirichlet L-functions.. |
13. |
Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya, Dirichlet Series with Periodic Coefficients and their Value-Distribution Near the Critical Line, Proceedings of the Steklov Institute of Mathematics, Analytic and Combinatorial Number Theory: Special issue in commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, 10.1134/S0081543821040118, 314, 1, 238-263, 2021.10. |
14. |
Daniel A. Goldston, Ade Irma Suriajaya, The error term in the Cesàro mean of the prime pair singular series, J. Number Theory, 10.1016/j.jnt.2021.03.004, 227, 144-157, 2021.10, 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.. |
15. |
Leonid G. Fel, Takao Komatsu, Ade Irma Suriajaya, A Sum of Negative Degrees of the Gaps Values in Two-Generated Numerical Semigroups and Identities for the Hurwitz Zeta Function, In: Nathanson M.B. (eds) Combinatorial and Additive Number Theory IV. CANT 2020. Springer Proceedings in Mathematics & Statistics, Springer, Cham., 10.1007/978-3-030-67996-5_8, 347, 151-160, 2021.08. |
16. |
Daniel A. Goldston, Ade Irma Suriajaya, A singular series average and the zeros of the Riemann zeta-function, Acta Arith., 10.4064/aa200821-24-2, 200, 71-90, 2021.06, 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-function. Unconditionally this error term can be shown to oscillate, while conditionally it can be shown to oscillate between sharp bounds.. |
17. |
Shōta Inoue, Sumaia Saad Eddin, Ade Irma Suriajaya, Stieltjes constants of $L$-functions in the extended Selberg class, Ramanujan J., 10.1007/s11139-021-00391-1, 55, 609-621, 2021.03. |
18. |
Leonid G. Fel, Takao Komatsu, Ade Irma Suriajaya, A sum of negative degrees of the gaps values in 2 and 3-generated numerical semigroups, Annales Mathematicae et Informaticae, 10.33039/ami.2020.08.001, 52, 85-95, 2020.09. |
19. |
Jörn Steuding, Ade Irma Suriajaya, Value-Distribution of the Riemann Zeta-Function along its Julia Lines, Comput. Methods Funct. Theory, 10.1007/s40315-020-00316-x, 20, 3-4, 389-401, 2020.04. |
20. |
Junghun Lee, Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya, The Values of the Riemann Zeta-Function on Discrete Sets, Advanced Studies in Pure Mathematics, Proceedings of Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto’s 60th birthday, 10.2969/aspm/08410315, 84, 315-334, 2020.04. |
21. |
Fan Ge, Ade Irma Suriajaya, Note on the number of zeros of $\zeta^{(k)}(s)$, Ramanujan J., 10.1007/s11139-019-00219-z, 55, 661-672, 2020.03, Assuming the Riemann hypothesis, we prove that $$ N_k(T) = \frac{T}{2\pi}\log \frac{T}{4\pi e} + O_k\left(\frac{\log{T}}{\log\log{T}}\right), $$ where $N_k(T)$ is the number of zeros of $\zeta^{(k)}(s)$ in the region $0 |
22. |
Hirotaka Akatsuka, Ade Irma Suriajaya, Zeros of the first derivative of Dirichlet L-functions, J. Number Theory, 10.1016/j.jnt.2017.08.023, 184, 300-329, 2018.03. |
23. |
Ade Irma Suriajaya, Two estimates on the distribution of zeros of the first derivative of Dirichlet L-functions under the generalized Riemann hypothesis, J. Théor. Nombres Bordeaux, 10.5802/jtnb.988, 29, 2, 471-502, 2017.05. |
24. |
Junghun Lee, Ade Irma Suriajaya, An ergodic value distribution of certain meromorphic functions, J. Math. Anal. Appl., 10.1016/j.jmaa.2016.07.064, 445, 1, 125-138, 2017.01. |
25. |
Junghun Lee, Tomokazu Onozuka, Ade Irma Suriajaya, Some probabilistic value distributions of the Riemann zeta function and its derivatives, Proc. Japan Acad. Ser. A Math. Sci., 10.3792/pjaa.92.82, 92, 7, 82-83, 2016.07. |
26. |
Ade Irma Suriajaya, On the zeros of the k-th derivative of the Riemann zeta function under the Riemann hypothesis, Funct. Approx. Comment. Math, 10.7169/facm/2015.53.1.5, 53, 1, 69-95, 2015.10. |