Daniel Loughran

Search results

• 2024

  Good reduction and cyclic covers

  Javanpeykar, A., Loughran, D. & Mathur, S., 31 Jan 2024, In: Journal of the Institute of Mathematics of Jussieu. 23, 1, p. 463-494 32 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Hypersurfaces 100%
  • Projective 50%
  • Finite Set 50%
  • Higher Dimensions 50%
  • Finiteness 50%

• Rationality and arithmetic of the moduli of abelian varieties

  Loughran, D. & Sankaran, G., 6 Sept 2024, (Acceptance date) In: Moduli.

  Research output: Contribution to journal › Article › peer-review

  Open Access
• 2023

  Distribution of genus numbers of abelian number fields

  Frei, C., Loughran, D. & Newton, R., 1 Jun 2023, In: Journal of the London Mathematical Society. 107, 6, p. 2197-2217 21 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Asymptotic Formula 100%
  • Galois Group 100%

• Frobenian multiplicative functions and rational points in fibrations

  Loughran, D. & Matthiesen, L., 16 Sept 2023, In: Journal of the European Mathematical Society. 26, 12, p. 4779-4830

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Fibration 100%
  • Rational Point 100%
  • Multiplicative Function 100%
  • Projective Space 50%
  • Group Element 50%

• The elliptic sieve and Brauer groups

  Bhakta, S., Loughran, D., Rydin Myerson, S. & Nakahara, M., 30 Jun 2023, In: Proceedings of the London Mathematical Society. 126, 6, p. 1884-1922 39 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Elliptic Curve 100%
  • Rational Point 50%
  2 Citations (SciVal)

  52 Downloads (Pure)
• 2022

  Multivariate normal distribution for integral points on varieties

  El-Baz, D., Loughran, D. & Sofos, E., 31 Dec 2022, In: Transactions of the American Mathematical Society. 375, 5, p. 3089-3128 40 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Multivariate Normal Distribution 100%
  • Covariance Matrix 50%
  • Integer 50%
  • Geometric Interpretation 50%
  4 Citations (SciVal)

  100 Downloads (Pure)

• Number fields with prescribed norms

  Frei, C., Loughran, D. & Newton, R., 14 Apr 2022, In: Commentarii Mathematici Helvetici. 97, 1, p. 138-181 44 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Finite Set 100%
  • Existence Result 100%
  • Galois Group 100%
  7 Citations (SciVal)

  82 Downloads (Pure)

• Quantitative arithmetic of diagonal degree 2 K3 surfaces

  Gvirtz, D., Loughran, D. & Nakahara, M., 31 Oct 2022, In: Mathematische Annalen. 384, p. 1-75

  Research output: Contribution to journal › Article › peer-review

  Open Access

  File

  • Arithmetic 100%
  • Diagonal 100%
  • Hasse Principle 100%
  • Odd Order 50%
  • Rational Point 50%
  2 Citations (SciVal)

  81 Downloads (Pure)

• Rank jumps on elliptic surfaces and the Hilbert property

  Loughran, D. & Salgado, C., 31 Dec 2022, In: Annales de l'institut Fourier. 72, 2, p. 617-638 22 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Elliptic Surfaces 100%
  5 Citations (SciVal)
• 2021

  An Erdős-Kac law for local solubility in families of varieties

  Loughran, D. & Sofos, E., 4 Jun 2021, In: Selecta Mathematica. 27, 3, 42.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Gaussian Distribution 100%
  • Probability Distribution 100%
  • Distribution Law 100%
  1 Citation (SciVal)

• Arithmetic hyperbolicity and a stacky Chevalley-Weil theorem

  Javanpeykar, A. & Loughran, D., 3 Apr 2021, In: Journal of the London Mathematical Society. 103, 3, p. 846-869 24 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Finiteness 100%
  • Hyperbolicity 100%
  • Algebraic Number Theory 100%
  • Surfaces Of General Type 100%
  10 Citations (SciVal)

  7 Downloads (Pure)

• Integral Hasse principle and strong approximation for Markoff surfaces

  Loughran, D. & Mitankin, V., 1 Sept 2021, In: International Mathematics Research Notices. 2021, 18, p. 14086–14122 37 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Hasse Principle 100%
  7 Citations (SciVal)
• 2020

  Brauer-Manin obstruction for Erdős-Straus surfaces

  Bright, M. J. & Loughran, D., 13 Aug 2020, In: Bulletin of the London Mathematical Society. 52, 4, p. 746-761 16 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Obstruction 100%
  • Hasse Principle 100%
  1 Citation (SciVal)

  2 Downloads (Pure)

• Inverse Galois problem for del Pezzo surfaces over finite fields

  Loughran, D. & Trepalin, A., 20 Aug 2020, In: Mathematical Research Letters. 27, 3, p. 845-853

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Finite Field 100%
  6 Citations (SciVal)

• Pseudo-split fibres and arithmetic surjectivity

  Loughran, D., Smeets, A. & Skorobogatov, A., 1 Jul 2020, In: Annales Scientifiques de l'École Normale Supérieure . 53, 4, p. 1037-1070 34 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access
  5 Citations (SciVal)
• 2019

  Del Pezzo surfaces over finite fields and their Frobenius traces

  Banwait, B., Fité, F. & Loughran, D., 1 Jul 2019, In: Mathematical Proceedings of the Cambridge Philosophical Society. 167, 1, p. 35-60 26 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Finite Field 100%
  • Cubic Surface 50%
  • Corrected Version 25%
  11 Citations (SciVal)

• Rational points and non-anticanonical height functions

  Frei, C. & Loughran, D., Aug 2019, In: Proceedings of the American Mathematical Society. 147, 8, p. 3209-3223 15 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Height Function 100%
  • Rational Point 100%
  • Asymptotic Behavior 33%
  • Projective 33%
  • Line Bundle 33%
  2 Citations (SciVal)
• 2018

  Good Reduction of Fano Threefolds and Sextic Surfaces

  Javanpeykar, A. & Loughran, D., 27 Apr 2018, In: Annali della Scuola Normale Superiore di Pisa. 18, 2, p. 509-535 27 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Abelian Variety 100%
  18 Citations (SciVal)

• Normes de droites sur les surfaces cubiques

  Colliot-thélène, J.-L. & Loughran, D., 14 Sept 2018, In: Pure and Applied Mathematics Quarterly. 13, 1, p. 123-130 8 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access
  1 Citation (SciVal)

• Rational points of bounded height on general conic bundle surfaces

  Frei, C., Loughran, D. & Sofos, E., 1 Aug 2018, In: Proceedings of the London Mathematical Society. 117, 2, p. 407-440 34 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Rational Point 100%
  • Wide Class 50%
  • Asymptotic Distribution 50%
  12 Citations (SciVal)

• Sieving rational points on varieties

  Browning, T. & Loughran, D., 18 Sept 2018, (E-pub ahead of print) In: Transactions of the American Mathematical Society. 371, 8, p. 5757-5785 29 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Rational Point 100%
  • Upper Bound 20%
  • Sharp Estimate 20%
  5 Citations (SciVal)

• The Hasse norm principle for abelian extensions

  Frei, C., Loughran, D. & Newton, R., 31 Dec 2018, In: American Journal of Mathematics. 140, 6, p. 1639-1685 47 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Harmonic Analysis 100%
  • Weak Approximation 100%
  • Finite Abelian Group 100%
  • Local Condition 100%
  15 Citations (SciVal)

• The number of varieties in a family which contain a rational point

  Loughran, D., 31 Oct 2018, In: Journal of the European Mathematical Society. 20, 10, p. 2539-2588 50 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Rational Point 100%
  • Harmonic Analysis 50%
  • Group Element 50%
  11 Citations (SciVal)

• Zero-loci of Brauer group elements on semi-simple algebraic groups

  Loughran, D., Takloo-bighash, R. & Tanimoto, S., 29 Nov 2018, (E-pub ahead of print) In: Journal of the Institute of Mathematics of Jussieu. p. 1-41 41 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access
  4 Citations (SciVal)
• 2017

  Complete intersections: moduli, Torelli, and good reduction

  Javanpeykar, A. & Loughran, D., 31 Aug 2017, In: Mathematische Annalen. 368, 3-4, p. 1191-1225 35 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Complete Intersection 100%
  • Main Result 50%
  • Arithmetic 50%
  • Projective Space 50%
  • Abelian Variety 50%
  25 Citations (SciVal)
• 2016

  Failures of weak approximation in families

  Bright, M. J., Browning, T. D. & Loughran, D., 1 Jul 2016, In: Compositio Mathematica. 152, 7, p. 1435-1475 41 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access
  30 Citations (SciVal)

• Fibrations with few rational points

  Loughran, D. & Smeets, A., 1 Oct 2016, In: Geometric and Functional Analysis. 26, 5, p. 1449-1482 34 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Fibration 100%
  • Rational Point 100%
  19 Citations (SciVal)

• The Hasse principle for lines on diagonal surfaces

  Jahnel, J. & Loughran, D., 1 Jan 2016, In: Mathematical Proceedings of the Cambridge Philosophical Society. 160, 1, p. 107-119 13 p.

  Research output: Contribution to journal › Article › peer-review
  1 Citation (SciVal)

• The moduli of smooth hypersurfaces with level structure

  Javanpeykar, A. & Loughran, D., 19 Dec 2016, (E-pub ahead of print) In: Manuscripta Mathematica. 154, 1-2, p. 13-22 9 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Hypersurfaces 100%
  • Level Structure 100%
  • Automorphism 25%
  • Trace Formula 25%
  • Homology 25%
  6 Citations (SciVal)

• Varieties with too many rational points

  Browning, T. D. & Loughran, D., 7 Oct 2016, In: Mathematische Zeitschrift. 285, 3-4, p. 1249-1267 19 p.

  Research output: Contribution to journal › Article › peer-review

  Open Access

  • Rational Point 100%
  • Total Number 50%
  11 Citations (SciVal)
• 2015

  Equivariant Compactifications of Two-Dimensional Algebraic Groups

  Derenthal, U. & Loughran, D., 1 Feb 2015, In: Proceedings of the Edinburgh Mathematical Society. 58, 1, p. 149-168 20 p.

  Research output: Contribution to journal › Article › peer-review

  • Equivariant 100%
  • Direct Product 100%
  • Compactifications 100%
  • Algebraic Groups 100%
  • Homogeneous Space 50%
  11 Citations (SciVal)

• Good reduction of algebraic groups and flag varieties

  Javanpeykar, A. & Loughran, D., 1 Feb 2015, In: Archiv der Mathematik. 104, 2, p. 133-143 11 p.

  Research output: Contribution to journal › Article › peer-review

  • Algebraic Groups 100%
  • Homogeneous Space 50%
  • Abelian Variety 50%
  13 Citations (SciVal)

• Rational points of bounded height and the Weil restriction

  Loughran, D., 1 Sept 2015, In: Israel Journal of Mathematics. 210, 1, p. 47-79 33 p.

  Research output: Contribution to journal › Article › peer-review

  • Rational Point 100%
  • Projective 50%
  • Counterexample 50%
  • Asymptotic Formula 50%
  5 Citations (SciVal)

• The Hasse Principle for Lines on del Pezzo Surfaces

  Jahnel, J. & Loughran, D., 27 Mar 2015, In: International Mathematics Research Notices. 2015, 23, p. 12877–12919 33 p.

  Research output: Contribution to journal › Article › peer-review

  • Cubic Surface 100%
  • Hasse Principle 100%
  • Arbitrary Number 50%
  • Complete Intersection 50%
  4 Citations (SciVal)
• 2012

  Manin's conjecture for a singular quartic del Pezzo surface

  Loughran, D., 14 Jun 2012, In: Journal of the London Mathematical Society. 86, 2, p. 558-584

  Research output: Contribution to journal › Article › peer-review

  • Linear Form 100%
  3 Citations (SciVal)
• 2011

  Manin’s conjecture for a singular sextic del Pezzo surface

  Loughran, D., 24 Jan 2011, In: Journal de Théorie des Nombres de Bordeaux. 22, 3, p. 675-701

  Research output: Contribution to journal › Article › peer-review

  • Explicit Expression 100%
  • Zeta-Functions 100%
  10 Citations (SciVal)
• 2010

  Singular del Pezzo surfaces that are equivariant compactifications

  Derenthal, U. & Loughran, D., 1 Dec 2010, In: Journal of Mathematical Sciences. 171, 6, p. 714-724

  Research output: Contribution to journal › Article › peer-review

  • Equivariant 100%
  • Compactifications 100%
  12 Citations (SciVal)