Siegfred Baluyot

activity

20182025

most citedAn unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function

9 citations · 10 across the 10 of their papers we have counts for

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11 papers · 1 filter

math.NT2025

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…

math.NT2025

Twisted moments of characteristic polynomials of random matrices in the unitary group

Siegfred Baluyot, Brian Conrey

Recently, Keating and the second author of this paper devised a heuristic for predicting asymptotic formulas for moments of the Riemann zeta-function $ζ (s)$ . Their approach indicat…

math.NT2025

Multiple Dirichlet series predictions for moments of $L$ -functions: unitary, symplectic and orthogonal examples

Siegfred Baluyot, Martin Čech

We devise heuristics using multiple Dirichlet series to predict asymptotic formulas for shifted moments of (1) the family of Dirichlet $L$ -functions of all even primitive character…

math.NT2025

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…

math.NT2023

Low-lying zeros of a large orthogonal family of automorphic $L$ -functions

Siegfred Baluyot, Vorrapan Chandee, Xiannan Li

We study a new orthogonal family of $L$ -functions associated with holomorphic Hecke newforms of level $q$ , averaged over $q ≍ Q$ . To illustrate our methods, we prove a one lev…

math.NT2023★ 9 cited

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…

math.NT2023

Sign changes of the error term in the Piltz divisor problem

Siegfred Baluyot, Cruz Castillo

We study the function $Δ_k(x):=\sum_{n\leq x} d_k(n) - \mbox{Res}_{s=1} ( ζ^k(s) x^s/s )$, where $k \geq 3$ is an integer, $d_{k} (n)$ is the $k$ -fold divisor function, and $ζ (s)$ is t…

math.NT2022

Moments of zeta and correlations of divisor-sums: stratification and Vandermonde integrals

Siegfred Baluyot, Brian Conrey

We refine a recent heuristic developed by Keating and the second author. Our improvement leads to a new integral expression for the conjectured asymptotic formula for shifted momen…

math.NT2022★ 1 cited

Twisted $2 k$ th moments of primitive Dirichlet $L$ -functions: beyond the diagonal

Siegfred Baluyot, Caroline L. Turnage-Butterbaugh

We study the family of Dirichlet $L$ -functions of all even primitive characters of conductor at most $Q$ , where $Q$ is a parameter tending to $\infty$ . For an arbitrary positive in…

math.NT2018

Dirichlet $L$ -functions of quadratic characters of prime conductor at the central point

Siegfred Baluyot, Kyle Pratt

We prove that more than nine percent of the central values $L (\frac{1}{2}, χ_{p})$ are non-zero, where $p \equiv 1 (mod 8)$ ranges over primes and $χ_{p}$ is the real primitive Dirichle…

math.NT2018

Small zeros of Dirichlet $L$ -functions of quadratic characters of prime modulus

Julio Andrade, Siegfred Baluyot

In this paper, we investigate the distribution of the imaginary parts of zeros near the real axis of Dirichlet $L$ -functions associated to the quadratic characters $χ_{p}(\cdot)=(\…

The Alternative Hypothesis for Zeros of the Riemann Zeta-Function

Twisted moments of characteristic polynomials of random matrices in the unitary group

Multiple Dirichlet series predictions for moments of L-functions: unitary, symplectic and orthogonal examples

Pair Correlation of Zeros of the Riemann Zeta Function I: Proportions of Simple Zeros and Critical Zeros

Low-lying zeros of a large orthogonal family of automorphic L-functions

An unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function

Sign changes of the error term in the Piltz divisor problem

Moments of zeta and correlations of divisor-sums: stratification and Vandermonde integrals

Twisted 2kth moments of primitive Dirichlet L-functions: beyond the diagonal

Dirichlet L-functions of quadratic characters of prime conductor at the central point

Small zeros of Dirichlet L-functions of quadratic characters of prime modulus

Multiple Dirichlet series predictions for moments of $L$ -functions: unitary, symplectic and orthogonal examples

Low-lying zeros of a large orthogonal family of automorphic $L$ -functions

Twisted $2 k$ th moments of primitive Dirichlet $L$ -functions: beyond the diagonal

Dirichlet $L$ -functions of quadratic characters of prime conductor at the central point

Small zeros of Dirichlet $L$ -functions of quadratic characters of prime modulus