EXPLICIT CALCULATIONS FOR SONO’S MULTIDIMENSIONAL SIEVE OF E2-NUMBERS

Authors

Daniel A. Goldston, San Jose State UniversityFollow
Apoorva Panidapu, Stanford University
Jordan Schettler, San Jose State UniversityFollow

Publication Date

11-1-2024

Document Type

Article

Publication Title

Mathematics of Computation

Volume

93

Issue

350

DOI

10.1090/mcom/3938

First Page

2943

Last Page

2958

Abstract

We derive explicit formulas for integrals of certain symmetric polynomials used in Keiju Sono’s multidimensional sieve of E2-numbers, i.e., integers which are products of two distinct primes. We use these computations to produce the currently best-known bounds for gaps between multiple E2- numbers. For example, we show there are infinitely many occurrences of four E2-numbers within a gap size of 94 unconditionally and within a gap size of 32 assuming the Elliott-Halberstam conjecture for primes and E2-numbers.

Department

Mathematics and Statistics

Recommended Citation

Daniel A. Goldston, Apoorva Panidapu, and Jordan Schettler. "EXPLICIT CALCULATIONS FOR SONO’S MULTIDIMENSIONAL SIEVE OF E2-NUMBERS" Mathematics of Computation (2024): 2943-2958. https://doi.org/10.1090/mcom/3938