6 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…
Explicit upper and lower bounds on certain functions related to for
Stephan Ramon Garcia, Loïc Grenié, Giuseppe Molteni
We provide explicit upper and lower bounds for certain commonly occurring expressions that involve the Riemann zeta function and its derivatives on . For example, this…
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…
A noncommutative generalization of Hunter's positivity theorem
Stephan Ramon Garcia, Jurij Volčič
Hunter proved that the complete homogeneous symmetric polynomials of even degree are positive definite. We prove a noncommutative generalization of this result, in which the scalar…
Hunter's positivity theorem and random vector norms
Ludovick Bouthat, Ángel Chávez, Stephan Ramon Garcia
A theorem of Hunter ensures that the complete homogeneous symmetric polynomials of even degree are positive definite functions. A probabilistic interpretation of Hunter's theorem s…
Norms on Complex Matrices Induced by Random Vectors
Ángel Chávez, Stephan Ramon Garcia, Jackson Hurley
We introduce a family of norms on the complex matrices. These norms arise from a probabilistic framework, and their construction and validation involve probability the…