3 citations · 8 across the 8 of their papers we have counts for
11 papers
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…
On Product Formulas of Guillera and Sondow
Shihan Kanungo, Jordan Schettler
In this note, we evaluate a multivariable family of infinite products which generalize Guillera's infinite product for , and Ser's formula (rediscovered by Sondow) for . We…
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…
Explicit Calculations for Sono's Multidimensional Sieve of -Numbers
Daniel A. Goldston, Apoorva Panidapu, Jordan Schettler
We derive explicit formulas for integrals of certain symmetric polynomials used in Keiju Sono's multidimensional sieve of -numbers, i.e., integers which are products of two di…
Small Gaps Between Three Almost Primes and Almost Prime Powers
Daniel A. Goldston, Apoorva Panidapu, Jordan Schettler
A positive integer is called an -number if it is the product of distinct primes. We prove that there are infinitely many triples of -numbers within a gap size of …
Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II
Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu +3
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erdős-Mirksy conjecture which…
Rational Hyperbolic Triangles and a Quartic Model of Elliptic Curves
Nicolas Brody, Jordan Schettler
The family of Euclidean triangles having some fixed perimeter and area can be identified with a subset of points on a nonsingular cubic plane curve, i.e., an elliptic curve; furthe…
Using Continued Fractions to Compute Iwasawa Lambda Invariants of Imaginary Quadratic Number Fields
Jordan Schettler
Let be a prime such that and has class number 1. Then Hirzebruch and Zagier noticed that the class number of $\mathbb{Q}…
Generalizations of Iwasawa's 'Riemann-Hurwitz' Formula for Cyclic p-Extensions of Number Fields
Jordan Schettler
We produce generalizations of Iwasawa's `Riemann-Hurwitz' formula for number fields. These generalizations apply to cyclic extensions of number fields of degree p^n for any positiv…
An Alternative Proof and Generalization of Ferrero's Computations of Iwasawa λ-Invariants
Jordan Schettler
We prove a slight generalization of Iwasawa's `Riemann-Hurwitz' formula for number fields and use it to generalize Ferrero's and Kida's well-known computations of Iwasawa λ-invaria…