We give an asymptotic formula for the number of biquadratic extensions of the rationals of bounded discriminant that fail the Hasse norm principle.
Nous donnons une formule asymptotique pour le nombre d’extensions biquadratiques du corps des rationnels de discriminant borné qui contredisent le principe de norme de Hasse.
Revised:
Accepted:
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Classification: 11N25, 11R16
Keywords: Hasse norm theorem, Biquadratic extensions, character sums
Author's affiliations:
@article{JTNB_2018__30_3_947_0, author = {Nick Rome}, title = {The {Hasse} {Norm} {Principle} {For} {Biquadratic} {Extensions}}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {947--964}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {30}, number = {3}, year = {2018}, doi = {10.5802/jtnb.1058}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1058/} }
TY - JOUR TI - The Hasse Norm Principle For Biquadratic Extensions JO - Journal de Théorie des Nombres de Bordeaux PY - 2018 DA - 2018/// SP - 947 EP - 964 VL - 30 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1058/ UR - https://doi.org/10.5802/jtnb.1058 DO - 10.5802/jtnb.1058 LA - en ID - JTNB_2018__30_3_947_0 ER -
Nick Rome. The Hasse Norm Principle For Biquadratic Extensions. Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 3, pp. 947-964. doi : 10.5802/jtnb.1058. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1058/
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