9 citations · 9 across the 7 of their papers we have counts for
8 papers
Bounds for the residue of Dedekind zeta functions under GRH and applications
Stephan Ramon Garcia, Loïc Grenié, Ethan Simpson Lee +1
Let be the residue at of the Dedekind zeta function of a number field . We prove explicit upper and lower bounds for under the Gen…
New zero-free regions for Dedekind zeta-functions at small and large ordinates
Sourabhashis Das, Swati Gaba, Ethan Simpson Lee +2
Given a number field , we obtain new and explicit zero-free regions for Dedekind zeta-functions of , which refine the previous works of Ahn--Kwon, Kadiri, and…
Explicit conditional bounds for the residue of a Dedekind zeta-function at
Stephan Ramon Garcia, Loïc Grenié, Ethan Simpson Lee +1
We prove new explicit conditional bounds for the residue at of the Dedekind zeta-function associated to a number field. Our bounds are concrete and all constants are presente…
Explicit upper bounds for the number of primes simultaneously representable by any set of irreducible polynomials
Matteo Bordignon, Ethan Simpson Lee
Using an explicit version of Selberg's upper sieve, we obtain explicit upper bounds for the number of such that a non-empty set of irreducible polynomials with i…
Explicit estimates for Artin -functions: Duke's short-sum theorem and Dedekind Zeta Residues
Stephan Ramon Garcia, Ethan Simpson Lee
Under GRH, we establish a version of Duke's short-sum theorem for entire Artin -functions. This yields corresponding bounds for residues of Dedekind zeta functions. All numerica…
An effective analytic formula for the number of distinct irreducible factors of a polynomial
Stephan Ramon Garcia, Ethan Simpson Lee, Josh Suh +1
We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors of a polynomial . We use an explicit version o…
Unconditional Explicit Mertens' Theorems for Number Fields and Dedekind Zeta Residue Bounds
Stephan Ramon Garcia, Ethan Simpson Lee
We obtain unconditional, effective number-field analogues of the three Mertens' theorems, all with explicit constants and valid for . Our error terms are explicitly bounde…
Explicit Mertens' Theorems for Number Fields
Stephan Ramon Garcia, Ethan Simpson Lee
Assuming the Generalized Riemann Hypothesis we obtain uniform, effective number-field analogues of Mertens' theorems.