1 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. 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.