11 citations · 34 across the 24 of their papers we have counts for
16 papers · 1 filter
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 -functions near the -line with a variety of zero-free regions and zero-density estimates. As an ap…
Zero density theorems for short intervals
Andrew Fiori
We provide explicit bounds on the number of zeros for in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proport…
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 and which provide superior exponential a…
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…
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…
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…
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 to bounds of the same type on both and .…
Families of -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 -congruence subgroups, are obtained…
Sharper bounds for the Chebyshev function
Andrew Fiori, Habiba Kadiri, Joshua Swidinsky
We improve the unconditional explicit bounds for the error term in the prime counting function . In particular, we prove that, for all , we have \[ \left| ψ(x)-x \right|…
The unbounded denominator conjecture for the noncongruence subgroups of index
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…
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…
Lower Bounds for the Least Prime in Chebotarev
Andrew Fiori
In this paper we show there exists an infinite family of number fields , Galois over , for which the smallest prime of which splits completely in $L…
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…
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…
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.
On The -Invariants of CM-Elliptic Curves Defined Over
Andrew Fiori
We characterize the possible reductions of -invariants of elliptic curves which admit complex multiplication by an order where the curve itself is defined over $\m…