PhD theses:

05. (2024.07.05, co-advisor with Gabor Wiese) Bryan W. Advocaat: Explicit overconvergence rates related to Eisenstein series.
04. (2020.10.09, co-advisor with Fabien Pazuki) Riccardo Pengo: Mahler measures, special values of L-functions and complex multiplication.
03. (2017.12.18) Dino Destefano: Investigating slopes of overconvergent modular forms.
02. (2014.12.11) Nadim Rustom: Algebra and arithmetic of modular forms.
01. (2009.11.20) Jonas B. Rasmussen: Higher congruences between modular forms.

Master's theses:

54. (In progress) Anna Mai Østergård:
53. (2024.06.21) Julie Gregersen: p-adic numbers and torsion points on elliptic curves.
52. (2024.06.21) Daniel Anders Wille Grunkin: p-adic numbers and Skolem's method.
51. (2024.06.21) Stine Langhede: Fermat's last theorem.
50. (2024.04.05) Bertram Koch-Larsen: A diophantine equation and the modular method.
49. (2024.01.12) Mikkel Hartmann: Modular forms of weight one and their relation to Galois representations.
48. (2024.01.12) Christine Mehlsen: Completions of number fields with an application to Thue's theorem.
47. (2023.08.25) Iman Abughoula: Arithmetic of elliptic curves over number fields.
46. (2023.06.23) Weijie Zhang: Global class field theory on number fields.
45. (2023.01.27) Marius Enevold Gjesme: Classical treatment of Fermat's last Theorem.
44. (2022.06.17) August Trier Nerenst Andersen: Representing primes by $x^2+ny^2$. An introduction to the Hilbert class field.
43. (2022.06.17) Rasmus Boldsen Lund: Elliptic curves over number fields: The weak Mordell-Weil theorem.
42. (2021.06.18) Tilde Nor Stadel Borum: Frobenius groups realized as Galois groups.
41. (2021.01.13) Patrick Christensen: Quadratic forms, class field theory and primes of the form $p = x^2 + ny^2$.
40. (2020.09.30) Peter Zarandy: An exposition of Iwasawa theory.
39. (2020.06.23) Andrea Galli: Inverse Galois theory and embedding problems.
38. (2019.06.17) Bryan William Advocaat: The congruent number problem and Tunnell's theorem.
37. (2018.08.24) Ulrik Christensen: The class number formula and Gauss' class number problem.
36. (2018.08.24) Hugrún Fjóla Hafsteinsdóttir: Fermat's Last Theorem for regular prime exponents.
35. (2018.08.24) Kenneth Jensen: The analytic class number formula for cyclotomic fields and Fermat's Last Theorem.
34. (2017.08.30) Mathias Jørgensen: Local class field theory.
33. (2017.03.21) Anna Berger Brusch: Kummer’s lemma and Fermat’s last theorem for regular primes.
32. (2016.10.31) Aage Kristoffer Holm Nielsen: Fermat's last theorem for regular primes assuming Kummer's lemma.
31. (2016.08.12) Peter Vang Uttenthal: Ramification in local fields.
30. (2016.08.01) Martin Stensgaard Vetter: Fermat's Last Theorem for regular primes and the infinitude of irregular primes.
29. (2016.05.12) Nicolas Bru Frantzen: The arithmetic of elliptic curves: Mordell's theorem.
28. (2016.03.29) Mikkel Bøhlers Nielsen: Fermat's last theorem for regular prime exponents.
27. (2015.02.09) Konstantinos Mitsainas: Constructions with straightedge and compass, and Galois theory.
26. (2014.07.01) Nikolaos Tsopanidis: Root numbers of elliptic curves.
25. (2014.03.21) Lise Volsing Smith: Fermat's last theorem for regular primes.
24. (2013.11.08) Helene Juncher: Catalan's conjecture.
23. (2012.07.05) Alexander Fick: Nilpotency class of Frobenius kernels. On finite groups admitting regular automorphisms of prime order.
22. (2012.07.05) Niels von Holck: Billings upper bound for the rank. Rank determinations for elliptic curves with Diophantine applications.
21. (2012.01.05) Christian Dalbjerg: On local-global principles in algebraic number theory.
20. (2010.06.30) Kåre Schou Gjaldbæk: Higher ramification groups and the Artin conductor. (Awarded the 2010 Danish Mathematical Society Master's Thesis Prize.)
19. (2009.12.17) Rune Harder Bak: On $\ell$-adic Galois representations associated to modular forms.
18. (2009.08.20) Lasse Arnsdorf Pedersen: Primality testning by elliptic curves.
17. (2009.04.02) Akemi Kuronuma Lauritzen: Classification of torsion subgroups of elliptic curves.
16. (2009.04.02) Mette Nørregård: Skolem's method applied to the theorem of Thue and Ramanujan's conjecture.
15. (2009.04.02) Christine Søndergaard: The Diophantine equation $b^2 X^4 - D Y^2 = 1$.
14. (2006.12.08) Anders Rehfeld: Catalans formodning. Et diofantisk problem.Catalan's conjecture. A Diophantine problem.
13. (2006.12.08) Katrine Juul Christiansen: Point counting on elliptic curves over F_p.
12. (2006.11.10) Morten Schrøder Larsen: Galois representations and modular forms.
11. (2006.11.03) (Main advisor: Tom Høholdt) Kristian Brander: An optimal unramified tower of algebraic function fields.
10. (2006.06.28) Ahmet Tas: Billing's upper bound for the rank of elliptic curves with applications.
09. (2006.06.28) Tine Rahbek Krog: Baker's method and Thue's equation.
08. (2005.07.15) Henrik Friis Christensen: The Artin conjecture and modular forms of weight 1.
07. (2005.06.30) Jonas Bjørn Rasmussen: Serre's conjectures and Ribet's theorem.
06. (2005.05.30) Anders Kølvraa: Eichler-Shimura congruences.
05. (2005.01.05) Anna Arnth-Jensen: Rank calculations and 2-descents for a class of elliptic curves.
04. (2005.01.05) Anette Nielsen: Mordell's theorem.
03. (2004.06.21) Sune Nørgård-Sørensen: Elliptic curves with complex multiplication and abelian extensions.
02. (2004.06.21) Bende Sylvan: Minkowski units and a theorem of Brumer.
01. (2001.06.29) Peder Frederiksen: Computation of Artin conductors.

Projects:

53. (In progress) Anton Fehnker: Modular forms.
52. (In progress) Lasse Sebastian Kjæmpe Nielsen: Elliptic curves.
51. (2024.04.04) Anton Fehnker: Explicit counting of ideals in general number fields.
50. (2024.01.25) Nicolai Sebastian Carstensen: Local class field theory.
49. (2023.01.20) Weijie Zhang: Local class field theory.
48. (2022.11.08) Iman Abughoula: Completions with applications.
47. (2022.11.04) Weijie Zhang: p-adic numbers and completions.
46. (2022.01.31) Marie Stuhr Kaltoft: Algebraic Number Theory.
45. (2022.01.31) Jonathan Tilling Niemann: Galois cohomology and local class field theory.
44. (2021.11.12) Markus Emil Jacobsen: Completions of number fields and applications.
43. (2021.11.12)  Esben Folke Ydesen: Completions of number fields and applications.
42. (2021.06.25) Emil Rugaard Wieser: Algebraic Number Theory.
41. (2021.06.16) Frederikke Skov Henriksen: Galois Theory.
40. (2020.11.02) Rasmus Frigaard Lemvig: Galois Theory.
39. (2020.10.28) Mads Bjerge Christensen: Galois representations.
38. (2020.01.24) Tim With Berland: Quadratic forms and the Hasse-Minkowski theorem.
37. (2020.01.24) Esben Folke Ydesen: Fermat's last theorem for regular primes and the infinitude of irregular primes.
36. (2019.06.21) Josefine Alberte Sjøstrøm: p-adic numbers.
35. (2019.06.21) Erik Lange: Galois representations and applications.
34. (2018.11.27) Mads Bjerge Christensen: Modular forms.
33. (2017.11.03) Erik Lange: The theorem of Hasse-Minkowski.
32. (2017.01.23)  Bjarke Østergård Nielsen: Fermat's last theorem and prime ideal decomposition in the ring of algebraic integers.
31. (2016.01.29) Jakob Studsgaard Bergqvist: An introduction to elliptic curves and their abelian group structure.
30. (2015.06.19) Ida Maria Christensen: Algebraic number theory.
29. (2015.03.18) Leonard Grohmann: Algebraic number theory.
28. (2015.03.18) Niels Hvitved: Algebraic number theory.
27. (2015.03.18) Maria Kaiktzoglou: Algebraic number theory.
26. (2015.02.24) Nicolas Bru Frantzen: Algebraic curves and varieties.
25. (2010.10.25) Christian Dalbjerg: Higher ramification groups and the theorem of Hasse-Arf.
24. (2010.10.11) Lucia Morotti: Mordell's theorem via Selmer groups.
23. (2010.02.26) Eske Sparsø: Modular mod $\ell$ Galois representations.
22. (2009.09.21) Kåre Schou Gjaldbæk: Elliptic curves.
21. (2008.07.28) Mette Nørregård: The theorem of Billing-Mahler.
20. (2008.06.10) Christine Søndergaard: Binary quadratic Diophantine equations.
19. (2007.08.17) Line Thorup: AKS primality testing.
18. (2007.08.17) Lasse Arnsdorf Pedersen: Agrawal-Kayak-Saxena primality testing.
17. (2006.03.28) Katrine Juul Christiansen: Classification of torsion groups of rational points on elliptic curves.
16. (2005.12.16) Kasper Maes: Continued fractions and an application.
15. (2005.10.14) Petur Birgir Petersen: Continued fractions and application to factorization of integers.
14. (2005.09.22) Christine Brygger Andreasen: Elliptic curves with torsion groups isomorphic to $\Z/2n \times \Z/2$.
13. (2005.08.16) Tine Rahbek Krog, Allan Mathorne Rasmussen: Classification of cyclic torsion groups of even order for rational elliptic curves.
12. (2005.06.29) Morten Jacob Nesgaard: Classification of torsion subgroups of rational points on elliptic curves.
11. (2005.06.29) Sandra Müller, Stefanie Zweifel: Theorem of Billing and Mahler.
10. (2005.06.17) Jes Kamstrup Hansen: Factorization via continued fractions.
09. (2005.06.15) Ahmet Tas: Factorization via continued fractions.
08. (2005.05.01) Jacob Neesgård: Factorization via continued fractions.
07. (2005.03.18) Rikke Eie: Factorization via continued fractions.
06. (2005.02.07) Lars Elmegaard-Fessel: Factorization via continued fractions.
05. (2004.05.04) Henrik Friis Christensen, Anders Rehfeld: Factorization - the method of the quadratic sieve.
04. (2004.05.03) Sune Nørgård-Sørensen: Binary quadratic forms and a surprising correspondence.
03. (2004.04.16) Anders Kølvraa: The weak Mordell-Weil Theorem.
02. (2004.03.15) Anna Arnth-Jensen: Classification of elliptic curves.
01. (2003.11.06) Esben Wendt Lorenzen: Kummer's theorem. A proof of Fermat's last theorem for regular exponents.

Bachelor projects:

51. (In progress) Jakob Kaalby Thomsen:
50. (In progress) Peter Lishmann Nielsen:
49. (In progress) Lisa Wolfson:
48. (2024.06.17) Sebastian Blink Wendelbo Rasmussen: Topics in inverse Galois theory.
47. (2023.11.06) Lasse Sebastian Kjæmpe Nielsen: Fermat's last theorem in the case of regular exponents.
46. (2023.06.29) Oscar Andreas Petri: Fermat's last theorem.
45. (2023.01.24) Markus Bay Graulund Slater: First case Fermat's theorem in classical treatment and prime regularity.
44. (2022.06.20) Erik Søndergaard Gimsing: The Galois theory of quintic polynomials.
43. (2022.06.20) Magnus Sejer Hansen: Inverse Galois theory.
42. (2022.06.20) Marie Stuhr Kaltoft: Realising Frobenius groups as Galois groups.
41. (2022.01.28) Nicolai Sebastian Carstensen: Completions.
40. (2022.01.28) Anna Mai Østergård: On $p$-adic numbers and Hasse-Minkowski's theorem.
39. (2021.06.28) Rasmus Frigaard Lemvig: Cubic and quartic reciprocity.
38. (2021.06.28) Christine Mehlsen: Algebraic number theory with applications.
37. (2021.01.28) Emil Rugaard Wieser: Ostrowski, Minkowski, Monsky: An introduction to $p$-adic numbers.
36. (2021.01.28) Tim With Berland: The Kronecker-Weber theorem.
35. (2020.06.19) Jonathan Tilling Niemann: The analytic class number formula.
34. (2020.06.19) Mads Emil Koefoed Rehof: Elliptic curves and the theorem of Hasse.
33. (2019.06.21) Mads Bjerge Christensen: Lifting of projective Galois representations.
32. (2018.08.24) Malte Kjellerup Juhl: Representation of integers by binary quadratic forms.
31. (2018.06.22) Freja Christine Slot Hansen: Primality testing in polynomial time.
30. (2017.06.23) Rasmus Kløvgaard Stavenuiter: Dirichlet's unit theorem.
29. (2016.06.20) Nina Mesing Stausholm Nielsen: RSA: Primality testing and prime factorization.
28. (2015.06.15) Mathias Jørgensen: Dirichlet's unit theorem.
27. (2015.06.15) Ane Carina Reiter: Bernoulli numbers, regular primes, and Fermat's last theorem.
26. (2015.03.27) Andreas Aachen (co-advisor: Peter Beelen, DTU): Algebraic function fields.
25. (2015.01.23) Ida Maria Christensen: Galois groups of polynomials of degree five.
24. (2014.06.20) Jakob Studsgaard Bergqvist: A special case of Fermat's last theorem and regular primes.
23. (2014.06.20) Martin Stemann Madsen: p-adic numbers: Construction and applications.
22. (2014.06.19) Alex Voigt Hansen: Elliptic curves and their application in cryptography.
21. (2014.06.18) Anne Gregersen: 1st case of Fermat's last theorem for regular primes.
20. (2014.01.24)  Kirsten Birkegaard Madsen: p-adic numbers.
19. (2012.06.21) Maria Kongshavn: Basic number theory and the first case of Fermat's last theorem.
18. (2012.06.21) Frederik Möllerström Lauridsen: The structure of the algebra of modular forms of level 1 modulo p.
17. (2012.06.21) Nor Stadel: The theorem of Hasse-Minkowski.
16. (2011.06.21) Roger Ten: A proof of Billing-Mahler's theorem.
15. (2011.06.21) Rasmus Pihl: Galois theory for polynomials of low degree.
14. (2010.11.05) Thomas Buron Glinski: Primality testing via elliptic curves.
13. (2010.06.25) Helene Juncher: p-adic numbers.
12. (2010.06.25) Tina Lysholm Hansen: On p-adic numbers and the theorem of Hasse-Mikowski on rational quadratic forms.
11. (2010.06.25) Martin Frank Hansen: Continued fractions.
10. (2010.01.28) Alexander Fick: AKS primality testing.
09. (2010.01.28) Asger Brix Jensen: Factorization via continued fractions.
08. (2009.01.21) Kristoffer Kjær: A proof of Mordell's theorem via Selmer groups.
07. (2009.01.21) Eske Sparsø: Elliptic curves and Selmer groups.
06. (2009.01.21) Christian Overgaard Lund: Weak Mordell via the theory of Selmer groups.
05. (2008.01.31) Martin Wedel Jacobsen: The theorem of Hasse-Minkowskis for rational quadratic forms.
04. (2006.08.18) Henrik Densing Pedersen: Torsion points on elliptic curves.
03. (2003.06.20) Mikkel Porse Rasmussen: Factorization via continued fractions.
02. (2003.01.21) Lars Bojsen-Møller: The Pohlig-Hellman algorithm for determination of the discrete logarithm and its application in cryptography.
01. (2002.06.24) Troels Windfeldt Hansen: On the algorithm of Ren\'{e} Schoof.