Loic Greni'e

Publications6
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Citations9
Highly Influential Citations0
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Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, II
We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.
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An improvement to an algorithm of Belabas, Diaz y Diaz and Friedman
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 field. Their… Expand
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Explicit Short Intervals for Primes in Arithmetic Progressions on GRH
We prove explicit versions of Cramer's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
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Primes in explicit short intervals on RH
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
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Conditional upper bound for the k-th prime ideal with given Artin symbol
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.
Counting Egyptian fractions
For any integer $N \geq 1$, let $\mathfrak{E}_N$ be the set of all Egyptian fractions employing denominators less than or equal to $N$. We give upper and lower bounds for the cardinality of… Expand