Zobrazeno 1 - 10
of 14
pro vyhledávání: '"Loïc André Henri Grenie"'
Publikováno v:
Journal of Number Theory. 200:441-485
We prove an explicit version of the Chebotarev theorem for the density of prime ideals with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions. In appendix we also give some explicit for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::109c6160e989ae3e56bd1bda160a1330
https://doi.org/10.1016/j.jnt.2018.12.005
https://doi.org/10.1016/j.jnt.2018.12.005
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.
Comment: We have improved the introduction and made clearer some c
Comment: We have improved the introduction and made clearer some c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef3414ccf87e54b7ff5a1bcdb965666e
http://arxiv.org/abs/1906.01994
http://arxiv.org/abs/1906.01994
We prove explicit versions of Cram\'er's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
Comment: A misprint in a formula has been corrected; all constants appearing in the conclusions have
Comment: A misprint in a formula has been corrected; all constants appearing in the conclusions have
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b379f3bf843cee80d1ad10b45c751c3
http://hdl.handle.net/10446/140234
http://hdl.handle.net/10446/140234
Publikováno v:
Mathematical Inequalities & Applications. :1427-1442
Let g(x):= (e/x)xΓ(x+1) and F(x,y):= g(x)g(y)/g(x+y). Let Dx,y (k) be the k th differential in Taylor's expansion of logF(x,y) . We prove that when (x,y) ∈ R+ 2 one has (-1)k-1Dx,y (k) (X,Y) > 0 for every X,Y ∈ R+, and that when k is even the co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::923252bb1e9d313744580966e751d1db
https://doi.org/10.7153/mia-18-111
https://doi.org/10.7153/mia-18-111
Publikováno v:
Funct. Approx. Comment. Math. 57, no. 1 (2017), 21-38
We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.
Comment: Followed referee's advice including changing title
Comment: Followed referee's advice including changing title
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a5bbd296a06aaa067a06185f3a6271db
https://doi.org/10.7169/facm/1611
https://doi.org/10.7169/facm/1611
Assuming Generalized Riemann's Hypothesis, Bach proved that the class group $\mathcal C\!\ell_{\mathbf K}$ of a number field ${\mathbf K}$ may be generated using prime ideals whose norm is bounded by $12\log^2\Delta_{\mathbf K}$, and by $(4+o(1))\log
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::351592e828e7d314cb0c88af72c9a60b
http://arxiv.org/abs/1607.02430
http://arxiv.org/abs/1607.02430
We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0754671031317619fd06198be1ac76f7
http://arxiv.org/abs/1602.02906
http://arxiv.org/abs/1602.02906
Autor:
Loïc André Henri Grenie
Publikováno v:
Journal de Théorie des Nombres de Bordeaux. 20:707-714
Soit K un corps de nombres contenant, pour un nombre premier l, les racines l-iemes de l'unite. Soit L une extension de Kummer de degre l de K, caracterisee par son module m et son groupe de normes. Soit K m le compositum des extensions de degre l de
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::556647b60c40e728ca28e7afd742d808
https://doi.org/10.5802/jtnb.646
https://doi.org/10.5802/jtnb.646
Let $\psi_\K$ be the Chebyshev function of a number field $\K$. Under GRH we prove an explicit upper bound for $|\psi_\K(x)-x|$ in terms of the degree and the discriminant of $\K$. The new bound improves significantly on previous known results.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a0ad0a1f0b9beded5792236ca1e510f
http://hdl.handle.net/10446/58029
http://hdl.handle.net/10446/58029
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
Comment: Corrected Corollary 4.1. Minor changes to the bibliography. To appear in Int. J. Number Theory
Comment: Corrected Corollary 4.1. Minor changes to the bibliography. To appear in Int. J. Number Theory
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf14592c8b0fbc23180a69c8a82a912a
http://hdl.handle.net/10446/58043
http://hdl.handle.net/10446/58043