10 citations · 61 across the 26 of their papers we have counts for
31 papers
One-level density of zeros of the Riemann zeta function weighted by its special values
Shingo Sugiyama, Ade Irma Suriajaya
We consider the one-level density of zeros of the Riemann zeta function weighted by its special values on the line , where is a fixed real number such that $1/2\…
A connection between low-lying zeros and central values of -functions
Didier Lesesvre, Ade Irma Suriajaya
We discuss the relation between statistics on low-lying zeros of -functions and distribution of the associated central values. More precisely, we deduce explicit conditional low…
Zeta Zeros in a Narrow Vertical Box
Daniel A. Goldston, Ade Irma Suriajaya
In 1973 Montgomery proved, assuming the Riemann Hypothesis (RH), that asymptotically at least 2/3 of zeros of the Riemann zeta-function are simple zeros. In a previous note (arXiv:…
Zeta Zeros on the Critical Line
Daniel A. Goldston, Ade Irma Suriajaya
Montgomery in 1973 introduced the pair correlation method to study the vertical distribution of Riemann zeta-function zeros. This work assumed the Riemann Hypothesis (RH). One stri…
The Alternative Hypothesis for Zeros of the Riemann Zeta-Function
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1
In 2016, the first-named author introduced a formulation of the Alternative Hypothesis that assumes that consecutive zeros of the Riemann zeta-function are spaced at multiples of h…
Pair Correlation Conjecture for the zeros of the Riemann zeta-function II: The Alternative Hypothesis
Daniel A. Goldston, Junghun Lee, Jordan Schettler +1
In an earlier paper, we proved that Montgomery's Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function can be used to prove without the assumption of the Riemann…
Pair Correlation Conjecture for the Zeros of the Riemann Zeta-function I: Simple and Critical Zeros
Daniel Alan Goldston, Junghun Lee, Jordan Schettler +1
Montgomery in 1973 introduced the Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function. He also conjectured that asymptotically 100% of the zeros are simple. Hi…
Pair Correlation of Zeros of the Riemann Zeta Function I: Proportions of Simple Zeros and Critical Zeros
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1
Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem in 1973 concerning the pair correlation of zeros of the Riemann zeta-function and applied this to prove that at le…
Conditional lower bounds on the distribution of central values: the case of modular forms
Didier Lesesvre, Ade Irma Suriajaya
Radziwill and Soundararajan unveiled a connection between low-lying zeros and central values of -functions, which they instantiated in the case of quadratic twists of an ellipti…
The average number of Goldbach representations over multiples of
Karin Ikeda, Ade Irma Suriajaya
We discuss the evaluation of the average number of Goldbach representations for integers which are multiples of introduced by Granville. We improve an estimate given by Granvil…
On a smoothed average of the number of Goldbach representations
Daniel A. Goldston, Ade Irma Suriajaya
Assuming the Generalized Riemann Hypothesis for the zeros of the Dirichlet -functions with characters modulo , we obtain a smoothed version of the average number of Goldbach…
An unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function
Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1
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, assumi…
The Average Number of Goldbach Representations and Zero-Free Regions of the Riemann Zeta-Function
Keith Billington, Maddie Cheng, Jordan Schettler +1
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 gener…
The Prime Number Theorem and Pair Correlation of Zeros of the Riemann Zeta-Function
D. A. Goldston, Ade Irma Suriajaya
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 cor…
The -points of the Riemann zeta-function and the functional equation
Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the -points of the zeta-function, i.e., the roots of the equa…
Zeros of derivatives of -functions in the Selberg class on
Sneha Chaubey, Suraj Singh Khurana, Ade Irma Suriajaya
In this article, we show that the Riemann hypothesis for an -function belonging to the Selberg class implies that all the derivatives of can have at most finitely many z…
Weighted one-level density of low-lying zeros of Dirichlet -functions
Shingo Sugiyama, Ade Irma Suriajaya
In this paper, we compute the one-level density of low-lying zeros of Dirichlet -functions in a family weighted by special values of Dirichlet -functions at a fixed $s \in [1…
On an Average Goldbach Representation Formula of Fujii
D. A. Goldston, Ade Irma Suriajaya
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 erro…
Note on the Goldbach Conjecture and Landau-Siegel Zeros
D. A. Goldston, Ade Irma Suriajaya
We generalize the work of Fei, Bhowmik and Halupczok, and Jia relating the Goldbach conjecture to real zeros of Dirichlet -functions.
Riemann-Type Functional Equations -- Julia Line and Counting Formulae --
Athanasios Sourmelidis, Jörn Steuding, Ade Irma Suriajaya
We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number …
A singular series average and the zeros of the Riemann zeta-function
D. A. Goldston, Ade Irma Suriajaya
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 expresse…
Value-Distribution of the Riemann Zeta-Function along its Julia Lines
Jörn Steuding, Ade Irma Suriajaya
For an arbitrary complex number we consider the distribution of values of the Riemann zeta-function at the -points of the function which appears in the functio…
Note on the number of zeros of
Fan Ge, Ade Irma Suriajaya
Assuming the Riemann hypothesis, we prove that where is the number of zeros of…
The error term in the Cesàro mean of the prime pair singular series
D. A. Goldston, Ade Irma Suriajaya
We show that the error term in the asymptotic formula for the Ces{à}ro mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures cannot be too sma…