Thu, 26 Jan 2023
16:00
L5

Distribution of genus numbers of abelian number fields

Rachel Newton
(King's College London)
Abstract

Let K be a number field and let L/K be an abelian extension. The genus field of L/K is the largest extension of L which is unramified at all places of L and abelian as an extension of K. The genus group is its Galois group over L, which is a quotient of the class group of L, and the genus number is the size of the genus group. We study the quantitative behaviour of genus numbers as one varies over abelian extensions L/K with fixed Galois group. We give an asymptotic formula for the average value of the genus number and show that any given genus number appears only 0% of the time. This is joint work with Christopher Frei and Daniel Loughran.

Improving the accuracy of biologically effective dose (BED) estimates, from a previously published study, after radiosurgery for acoustic neuromas
 Hopewell, J Moore, J Villafuerte, C Paddick, I Jones, B Hill, M Tsang, D World Neurosurgery volume 172 e130-e143 (29 Dec 2022)
Insect-scale jumping robots enabled by a dynamic buckling cascade
 Wang, Y Wang, Q Liu, M Qin, Y Cheng, L Bolminn, O Alleyne, M Wissa, A Baughman, R Vella, D Tawfick, S Proceedings of the National Academy of Sciences volume 120 issue 5 (31 Jan 2023)
Predicting phenotype transition probabilities via conditional algorithmic probability approximations
 Dingle, K Novev, J Ahnert, S Louis, A Journal of the Royal Society: Interface volume 19 issue 197 (14 Dec 2022)
Contact-number-driven virus evolution: a multi-level modeling framework for the evolution of acute or persistent RNA virus infection
 Sunagawa, J Komorizono, R Hart, W Thompson, R Makino, A Tomonaga, K Iwami, S Yamaguchi, R (01 Jan 2022)
Squarefrees are Gaussian in short intervals
 Gorodetsky, O Mangerel, A Rodgers, B Journal fuer die Reine und Angewandte Mathematik: Crelle's journal volume 2023 issue 795 1-44 (2023)
Concentration-dependent domain evolution in reaction–diffusion systems
 Krause, A Gaffney, E Walker, B Bulletin of Mathematical Biology volume 85 (13 Jan 2023)
The Deep Dementia Phenotyping (DEMON) Network: A global platform for innovation using data science and artificial intelligence
 Ranson, J Al Khleifat, A Lyall, D Newby, D Winchester, L Proitsi, P Veldsman, M Rittman, T Marzi, S Yao, Z Skene, N Bettencourt, C Kormilitzin, A Foote, I Golborne, C Lourida, I Bucholc, M Tang, E Oxtoby, N Bagshaw, P Walker, Z Everson, R Ballard, C van Duijn, C Langa, K MacLeod, M Rockwood, K Llewellyn, D Alzheimer's & Dementia volume 18 issue S2 (20 Dec 2022)
Discrimination of muons for mass composition studies of inclined air showers detected with IceTop
 Abbasi, R Ackermann, M Adams, J Aguilar, J Ahlers, M Ahrens, M Alispach, C Alves, A Amin, N An, R Andeen, K Anderson, T Anton, G Argüelles, C Ashida, Y Axani, S Bai, X Balagopal, A Barbano, A Barwick, S Bastian, B Basu, V Baur, S Bay, R Beatty, J Becker, K Becker Tjus, J Bellenghi, C BenZvi, S Berley, D Bernardini, E Besson, D Binder, G Bindig, D Blaufuss, E Blot, S Boddenberg, M Bontempo, F Borowka, J Böser, S Botner, O Böttcher, J Bourbeau, E Bradascio, F Braun, J Bron, S Brostean-Kaiser, J Browne, S Burgman, A Burley, R Busse, R Campana, M Carnie-Bronca, E Chen, C Chirkin, D Choi, K Clark, B Clark, K Classen, L Coleman, A Collin, G Conrad, J Coppin, P Correa, P Cowen, D Cross, R Dappen, C Dave, P De Clercq, C DeLaunay, J Dembinski, H Deoskar, K De Ridder, S Desai, A Desiati, P de Vries, K de Wasseige, G de With, M DeYoung, T Dharani, S Diaz, A Díaz-Vélez, J Dittmer, M Dujmovic, H Dunkman, M DuVernois, M Dvorak, E Ehrhardt, T Eller, P Engel, R Erpenbeck, H Evans, J Evenson, P Fan, K Fazely, A Fiedlschuster, S Fienberg, A Filimonov, K Finley, C Fischer, L Proceedings of Science volume 395 (18 Mar 2022)
Lorentz Meets Lipschitz
 Lange, C Lytchak, A Sämann, C Advances in Theoretical and Mathematical Physics volume 25 issue 8 2141-2170 (2021)
Subscribe to