---
_id: '13973'
abstract:
- lang: eng
  text: We construct families of log K3 surfaces and study the arithmetic of their
    members. We use this to produce explicit surfaces with an order 5 Brauer–Manin
    obstruction to the integral Hasse principle.
acknowledgement: "This paper was completed as part of a project which received funding
  from the\r\nEuropean Union’s Horizon 2020 research and innovation programme under
  the Marie\r\nSkłodowska-Curie grant agreement No. 754411."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Julian
  full_name: Lyczak, Julian
  id: 3572849A-F248-11E8-B48F-1D18A9856A87
  last_name: Lyczak
citation:
  ama: Lyczak J. Order 5 Brauer–Manin obstructions to the integral Hasse principle
    on log K3 surfaces. <i>Annales de l’Institut Fourier</i>. 2023;73(2):447-478.
    doi:<a href="https://doi.org/10.5802/aif.3529">10.5802/aif.3529</a>
  apa: Lyczak, J. (2023). Order 5 Brauer–Manin obstructions to the integral Hasse
    principle on log K3 surfaces. <i>Annales de l’Institut Fourier</i>. Association
    des Annales de l’Institut Fourier. <a href="https://doi.org/10.5802/aif.3529">https://doi.org/10.5802/aif.3529</a>
  chicago: Lyczak, Julian. “Order 5 Brauer–Manin Obstructions to the Integral Hasse
    Principle on Log K3 Surfaces.” <i>Annales de l’Institut Fourier</i>. Association
    des Annales de l’Institut Fourier, 2023. <a href="https://doi.org/10.5802/aif.3529">https://doi.org/10.5802/aif.3529</a>.
  ieee: J. Lyczak, “Order 5 Brauer–Manin obstructions to the integral Hasse principle
    on log K3 surfaces,” <i>Annales de l’Institut Fourier</i>, vol. 73, no. 2. Association
    des Annales de l’Institut Fourier, pp. 447–478, 2023.
  ista: Lyczak J. 2023. Order 5 Brauer–Manin obstructions to the integral Hasse principle
    on log K3 surfaces. Annales de l’Institut Fourier. 73(2), 447–478.
  mla: Lyczak, Julian. “Order 5 Brauer–Manin Obstructions to the Integral Hasse Principle
    on Log K3 Surfaces.” <i>Annales de l’Institut Fourier</i>, vol. 73, no. 2, Association
    des Annales de l’Institut Fourier, 2023, pp. 447–78, doi:<a href="https://doi.org/10.5802/aif.3529">10.5802/aif.3529</a>.
  short: J. Lyczak, Annales de l’Institut Fourier 73 (2023) 447–478.
date_created: 2023-08-06T22:01:12Z
date_published: 2023-05-12T00:00:00Z
date_updated: 2023-12-13T12:03:04Z
day: '12'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/aif.3529
ec_funded: 1
external_id:
  arxiv:
  - '2005.14013'
  isi:
  - '001000279500001'
file:
- access_level: open_access
  checksum: daf53fc614c894422e4c0fb3d2a2ae3e
  content_type: application/pdf
  creator: dernst
  date_created: 2023-08-07T07:19:42Z
  date_updated: 2023-08-07T07:19:42Z
  file_id: '13977'
  file_name: 2023_AnnalesFourier_Lyczak.pdf
  file_size: 1529821
  relation: main_file
  success: 1
file_date_updated: 2023-08-07T07:19:42Z
has_accepted_license: '1'
intvolume: '        73'
isi: 1
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '05'
oa: 1
oa_version: Published Version
page: 447-478
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Annales de l'Institut Fourier
publication_identifier:
  issn:
  - 0373-0956
publication_status: published
publisher: Association des Annales de l'Institut Fourier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Order 5 Brauer–Manin obstructions to the integral Hasse principle on log K3
  surfaces
tmp:
  image: /image/cc_by_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
  name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
  short: CC BY-ND (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 73
year: '2023'
...
---
_id: '2740'
abstract:
- lang: eng
  text: We show that the lowest eigenvalue of the magnetic Schrödinger operator on
    a line bundle over a compact Riemann surface M is bounded by the L1-norm of the
    magnetic field B. This implies a similar bound on the multiplicity of the ground
    state. An example shows that this degeneracy can indeed be comparable with ∫M
    |B| even in case of the trivial bundle.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Erdös L. Spectral shift and multiplicity of the first eigenvalue of the magnetic
    Schrödinger operator in two dimensions. <i>Annales de l’Institut Fourier</i>.
    2002;52(6):1833-1874. doi:<a href="https://doi.org/10.5802/aif.1936">10.5802/aif.1936</a>
  apa: Erdös, L. (2002). Spectral shift and multiplicity of the first eigenvalue of
    the magnetic Schrödinger operator in two dimensions. <i>Annales de l’Institut
    Fourier</i>. Association des Annales de l’Institut Fourier. <a href="https://doi.org/10.5802/aif.1936">https://doi.org/10.5802/aif.1936</a>
  chicago: Erdös, László. “Spectral Shift and Multiplicity of the First Eigenvalue
    of the Magnetic Schrödinger Operator in Two Dimensions.” <i>Annales de l’Institut
    Fourier</i>. Association des Annales de l’Institut Fourier, 2002. <a href="https://doi.org/10.5802/aif.1936">https://doi.org/10.5802/aif.1936</a>.
  ieee: L. Erdös, “Spectral shift and multiplicity of the first eigenvalue of the
    magnetic Schrödinger operator in two dimensions,” <i>Annales de l’Institut Fourier</i>,
    vol. 52, no. 6. Association des Annales de l’Institut Fourier, pp. 1833–1874,
    2002.
  ista: Erdös L. 2002. Spectral shift and multiplicity of the first eigenvalue of
    the magnetic Schrödinger operator in two dimensions. Annales de l’Institut Fourier.
    52(6), 1833–1874.
  mla: Erdös, László. “Spectral Shift and Multiplicity of the First Eigenvalue of
    the Magnetic Schrödinger Operator in Two Dimensions.” <i>Annales de l’Institut
    Fourier</i>, vol. 52, no. 6, Association des Annales de l’Institut Fourier, 2002,
    pp. 1833–74, doi:<a href="https://doi.org/10.5802/aif.1936">10.5802/aif.1936</a>.
  short: L. Erdös, Annales de l’Institut Fourier 52 (2002) 1833–1874.
date_created: 2018-12-11T11:59:21Z
date_published: 2002-01-01T00:00:00Z
date_updated: 2023-07-18T08:38:34Z
day: '01'
doi: 10.5802/aif.1936
extern: '1'
intvolume: '        52'
issue: '6'
language:
- iso: eng
month: '01'
oa_version: None
page: 1833-1874
publication: Annales de l'Institut Fourier
publication_identifier:
  issn:
  - 0373-0956
publication_status: published
publisher: Association des Annales de l'Institut Fourier
publist_id: '4152'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Spectral shift and multiplicity of the first eigenvalue of the magnetic Schrödinger
  operator in two dimensions
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 52
year: '2002'
...
---
_id: '2733'
abstract:
- lang: eng
  text: The Li-Yau semiclassical lower bound for the sum of the first N eigenvalues
    of the Dirichlet–Laplacian is extended to Dirichlet–Laplacians with constant magnetic
    fields. Our method involves a new diamagnetic inequality for constant magnetic
    fields.
article_processing_charge: No
article_type: original
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Michael
  full_name: Loss, Michael
  last_name: Loss
- first_name: Vitali
  full_name: Vougalter, Vitali
  last_name: Vougalter
citation:
  ama: Erdös L, Loss M, Vougalter V. Diamagnetic behavior of sums Dirichlet eigenvalues.
    <i>Annales de l’Institut Fourier</i>. 2000;50(3):891-907. doi:<a href="https://doi.org/10.5802/aif.1777">10.5802/aif.1777</a>
  apa: Erdös, L., Loss, M., &#38; Vougalter, V. (2000). Diamagnetic behavior of sums
    Dirichlet eigenvalues. <i>Annales de l’Institut Fourier</i>. Association des Annales
    de l’Institut Fourier. <a href="https://doi.org/10.5802/aif.1777">https://doi.org/10.5802/aif.1777</a>
  chicago: Erdös, László, Michael Loss, and Vitali Vougalter. “Diamagnetic Behavior
    of Sums Dirichlet Eigenvalues.” <i>Annales de l’Institut Fourier</i>. Association
    des Annales de l’Institut Fourier, 2000. <a href="https://doi.org/10.5802/aif.1777">https://doi.org/10.5802/aif.1777</a>.
  ieee: L. Erdös, M. Loss, and V. Vougalter, “Diamagnetic behavior of sums Dirichlet
    eigenvalues,” <i>Annales de l’Institut Fourier</i>, vol. 50, no. 3. Association
    des Annales de l’Institut Fourier, pp. 891–907, 2000.
  ista: Erdös L, Loss M, Vougalter V. 2000. Diamagnetic behavior of sums Dirichlet
    eigenvalues. Annales de l’Institut Fourier. 50(3), 891–907.
  mla: Erdös, László, et al. “Diamagnetic Behavior of Sums Dirichlet Eigenvalues.”
    <i>Annales de l’Institut Fourier</i>, vol. 50, no. 3, Association des Annales
    de l’Institut Fourier, 2000, pp. 891–907, doi:<a href="https://doi.org/10.5802/aif.1777">10.5802/aif.1777</a>.
  short: L. Erdös, M. Loss, V. Vougalter, Annales de l’Institut Fourier 50 (2000)
    891–907.
date_created: 2018-12-11T11:59:19Z
date_published: 2000-01-01T00:00:00Z
date_updated: 2023-05-03T08:56:17Z
day: '01'
doi: 10.5802/aif.1777
extern: '1'
intvolume: '        50'
issue: '3'
language:
- iso: eng
month: '01'
oa_version: None
page: 891 - 907
publication: Annales de l'Institut Fourier
publication_identifier:
  issn:
  - 0373-0956
publication_status: published
publisher: Association des Annales de l'Institut Fourier
publist_id: '4159'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Diamagnetic behavior of sums Dirichlet eigenvalues
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 50
year: '2000'
...