7 citations · 12 across the 5 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…
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…
Breaking the 4 barrier for the bound of a generating set of the class group
Loïc Grenié, Giuseppe Molteni
Let be a field of degree and discriminant with absolute value . Under the assumption of the validity of the Generalized Riemann Hypothesis, we provide a new algorithm to…
Conditional upper bound for the k-th prime ideal with given Artin symbol
Loïc Grenié, Giuseppe Molteni
We prove an explicit upper bound for the k-th prime ideal with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.
Explicit Short Intervals for Primes in Arithmetic Progressions on GRH
Adrian W. Dudek, Loïc Grenié, Giuseppe Molteni
We prove explicit versions of Cramér's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
Primes and prime ideals in short intervals
L. Grenié, G. Molteni, A. Perelli
We prove the analog of Cramér's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in t…
An improvement to an algorithm of Belabas, Diaz y Diaz and Friedman
Loïc Grenié, Giuseppe Molteni
In [BDyDF08] Belabas, Diaz y Diaz and Friedman show a way to determine, assuming the Generalized Riemann Hypothesis, a set of prime ideals that generate the class group of a number…