A. Fiori

activity

20152026

most citedStrengthening the Baillie-PSW primality test

11 citations · 34 across the 24 of their papers we have counts for

collaborators

24 papers

math.NT2026

Explicit bounds for the prime number theorem

Andrew Fiori, Mikko Jaskari

We study the problem of finding tight explicit bounds on sums over zeros of $L$ -functions near the $1$ -line with a variety of zero-free regions and zero-density estimates. As an ap…

math.NT2026

Zero density theorems for short intervals

Andrew Fiori

We provide explicit bounds on the number of zeros for $ζ$ in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proport…

math.NT2026

Bounds for Mertens Sums

Samuel Broadbent, Andrew Fiori, Habiba Kadiri +2

In this article we provide new bounds for the Mertens sums and products including $\sum_{p \leq x} p^{- 1}$ and $\prod_{p \leq x} (1 - \frac{1}{p})$ which provide superior exponential a…

math.NT2025

Counting Frobenius Pseudoprimes

Andrew Fiori, Hiva Gheisari

We generalize the work of Erdos-Pomerance and Fiori-Shallue on counting Frobenius pseudoprimes from the cases of degree one and two respectively to arbitrary degree. More specifica…

math.NT2025

A Note on the Phragmen-Lindelof Theorem

Andrew Fiori

We provide a generalization of the Phragmén-Lindelöf principal of Rademacher with the aim of correcting, or at least provide a pathway to correcting, several errors appearing in th…

math.NT2024

The Least Prime in Arithmetic an Progression

Andrew Fiori

In his 1979 paper Samuel Wagstaff studied the problem of bounding the first prime in an arithmetic progression. In this paper we update a number of his computations using advances…

math.NT2022

Sharper bounds for the error term in the Prime Number Theorem

Andrew Fiori, Habiba Kadiri, Joshua Swidinsky

We provide very effective methods to convert both asymptotic and explicit numeric bounds on the prime counting function $ψ (x)$ to bounds of the same type on both $θ (x)$ and $π (x)$ .…

math.NT2022

Families of $ϕ$ -congruence subgroups of the modular group

Angelica Babei, Andrew Fiori, Cameron Franc

We introduce and study families of finite index subgroups of the modular group that generalize the congruence subgroups. Such groups, termed $ϕ$ -congruence subgroups, are obtained…

math.NT2022

Sharper bounds for the Chebyshev function $ψ (x)$

Andrew Fiori, Habiba Kadiri, Joshua Swidinsky

We improve the unconditional explicit bounds for the error term in the prime counting function $ψ (x)$ . In particular, we prove that, for all $x > 2$ , we have \[ \left| ψ(x)-x \right|…

math.RT2021★ 3 cited

Appearance of the Kashiwara-Saito singularity in the representation theory of $p$ -adic $G L_{16}$

Clifton Cunningham, Andrew Fiori, Nicole Kitt

In 1993 David Vogan proposed a basis for the vector space of stable distributions on $p$ -adic groups using the microlocal geometry of moduli spaces of Langlands parameters. In the…

math.RT2021

Toward the endoscopic classification of unipotent representations of $p$ -adic $G_{2}$

Clifton Cunningham, Andrew Fiori, Qing Zhang

We begin this paper by reviewing the Langlands correspondence for unipotent representations of the exceptional group of type $G_{2}$ over a $p$ -adic field $F$ and present it in an ex…

math.NT2020★ 1 cited

The unbounded denominator conjecture for the noncongruence subgroups of index $7$

Andrew Fiori, Cameron Franc

We study modular forms for the minimal index noncongruence subgroups of the modular group. Our main theorem is a proof of the unbounded denominator conjecture for these groups, and…

math.NT2020★ 11 cited

Strengthening the Baillie-PSW primality test

Robert Baillie, Andrew Fiori, Samuel S. Wagstaff

The Baillie-PSW primality test combines Fermat and Lucas probable prime tests. It reports that a number is either composite or probably prime. No odd composite integer has been rep…

math.RT2020★ 6 cited

Arthur packets for $G_{2}$ and perverse sheaves on cubics

Clifton Cunningham, Andrew Fiori, Qing Zhang

This paper begins the project of defining Arthur packets of all unipotent representations for the $p$ -adic exceptional group $G_{2}$ . Here we treat the most interesting case by defin…

math.AG2019

Embeddings of maximal tori in groups of type $F_{4}$

Andrew Fiori, Federico Scavia

We classify maximal tori in groups of type $F_{4}$ over a local or global field of characteristic different from $2$ and $3$ . We prove a local-global principle for embeddings of maxi…

math.NT2018★ 3 cited

Lower Bounds for the Least Prime in Chebotarev

Andrew Fiori

In this paper we show there exists an infinite family of number fields $L$ , Galois over $Q$ , for which the smallest prime $p$ of $Q$ which splits completely in $L…

math.NT2017★ 2 cited

Average liar count for degree-2 Frobenius pseudoprimes

Andrew Fiori, Andrew Shallue

In this paper we obtain lower and upper bounds on the average number of liars for the Quadratic Frobenius Pseudoprime Test of Grantham, generalizing arguments of Erdős and Pomeranc…

math.RT2017★ 2 cited

Arthur packets for $p$ -adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples

Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui +2

In this article we propose a geometric description of Arthur packets for $p$ -adic groups using vanishing cycles of perverse sheaves. Our approach is inspired by the 1992 book by Ad…

math.GR2017★ 1 cited

Rational Conjugacy Classes of Maximal Tori In Groups of Type $D_{n}$

Andrew Fiori

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type $D_{n}$ , with specific emphasis on the case of number fields and p-adic fields…

math.NT2016

Toroidal Compactifications and Dimension Formulas for Spaces of Modular Forms for Orthogonal Shimura Varieties

Andrew Fiori

In this paper we describe the general theory of constructing toroidal compactifications of locally symmetric spaces and using these to compute dimension formulas for spaces of modu…

math.NT2016★ 1 cited

Sub-Shimura Varieties for type O(2,n)

Andrew Fiori

We give a classification, up to consideration of component groups, of sub-Shimura varieties of those Shimura Varieties attached to orthogonal groups of signature (2,n) over Q.

math.AG2015★ 1 cited

A Riemann-Hurwitz Theorem for the Algebraic Euler Characteristic

Andrew Fiori

We prove an analogue of the Riemann-Hurwitz theorem for computing Euler characteristics of pullbacks of coherent sheaves through finite maps of smooth projective varieties, subject…

math.NT2015

On The $j$ -Invariants of CM-Elliptic Curves Defined Over $Z_{p}$

Andrew Fiori

We characterize the possible reductions of $j$ -invariants of elliptic curves which admit complex multiplication by an order $O$ where the curve itself is defined over $\m…

math.GR2015★ 3 cited

Classification of Certain Subgroups of G2

Andrew Fiori

We give a concrete characterization of the rational conjugacy classes of maximal tori in groups of type G2, focusing on the case of number fields and p-adic fields. In the same con…

Explicit bounds for the prime number theorem

Zero density theorems for short intervals

Bounds for Mertens Sums

Counting Frobenius Pseudoprimes

A Note on the Phragmen-Lindelof Theorem

The Least Prime in Arithmetic an Progression

Sharper bounds for the error term in the Prime Number Theorem

Families of ϕ-congruence subgroups of the modular group

Sharper bounds for the Chebyshev function ψ(x)

Appearance of the Kashiwara-Saito singularity in the representation theory of p-adic GL16​

Toward the endoscopic classification of unipotent representations of p-adic G2​

The unbounded denominator conjecture for the noncongruence subgroups of index 7

Strengthening the Baillie-PSW primality test

Arthur packets for G2​ and perverse sheaves on cubics

Embeddings of maximal tori in groups of type F4​

Lower Bounds for the Least Prime in Chebotarev

Average liar count for degree-2 Frobenius pseudoprimes

Arthur packets for p-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples

Rational Conjugacy Classes of Maximal Tori In Groups of Type Dn​

Toroidal Compactifications and Dimension Formulas for Spaces of Modular Forms for Orthogonal Shimura Varieties

Sub-Shimura Varieties for type O(2,n)

A Riemann-Hurwitz Theorem for the Algebraic Euler Characteristic

On The j-Invariants of CM-Elliptic Curves Defined Over Zp​

Classification of Certain Subgroups of G2

Families of $ϕ$ -congruence subgroups of the modular group

Sharper bounds for the Chebyshev function $ψ (x)$

Appearance of the Kashiwara-Saito singularity in the representation theory of $p$ -adic $G L_{16}$

Toward the endoscopic classification of unipotent representations of $p$ -adic $G_{2}$

The unbounded denominator conjecture for the noncongruence subgroups of index $7$

Arthur packets for $G_{2}$ and perverse sheaves on cubics

Embeddings of maximal tori in groups of type $F_{4}$

Arthur packets for $p$ -adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples

Rational Conjugacy Classes of Maximal Tori In Groups of Type $D_{n}$

On The $j$ -Invariants of CM-Elliptic Curves Defined Over $Z_{p}$