I am Martin Raum, Associate Professor at Chalmers Technical University in Gothenburg, Sweden.

My major research interests are modular forms and their applications in mathematics and physics:

  • Applications of automorphic forms.
  • Cohomological automorphic forms and their generalizations.
  • Siegel and orthogonal modular forms.
  • Explicit methods for automorphic forms.

Research

Some of my publications come along with software or data. See the download section.

Note that the versions of my paper on arXiv or HAL usually do not coincide with published revisions, if not indicated otherwise. For some journals, I strongly recommend to use the arXiv version.

Research Publications

  1. The skew-Maass lift I.
    Joint with Olav Richter.
    Res. Math. Sci. 6.2 (2019) and arXiv 1810.06810 (2018).

  2. Hyper-Algebras of Vector-Values Modular Forms.
    SIGMA 14.108 (2018) and HAL-01289143 (2016).

  3. Indecomposable Harish-Chandra modules for Jacobi groups
    Contributions in Mathematical and Computational Sciences 10 (2017).

  4. On Direct Integration for Mirror Curves of Genus Two and an Almost Mromorphic Siegel Modular Form.
    Joint with Albrecht Klemm, Maximilian Poretschkin, and Thorsten Schimannek.
    Commun. Number Theory Phys. 10.4 (2016) and arXiv 1502.00557 (2015).

  5. Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms.
    Joint with Kathrin Bringmann and Olav Richter.
    Res. Math. Sci. 3.30 (2016) and arXiv 1604.05105 (2016).

  6. Harmonic Weak Siegel Maass Forms I.
    Int. Math. Res. Not. (2016) and arXiv 1510.03342 (2015).

  7. Products of Vector Valued Eisenstein Series.
    Forum Math. 29.1 (2017), pp. 157–186 and arXiv 1411.3877 (2014).

  8. Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices.
    Joint with Charles Conley
    Int. J. Number Theory 12.07 (2016) and arXiv 1012.2897 (2010).

  9. Computing Genus 1 Jacobi Forms.
    Math. Comp. 85 (2016) pp. 931-960 and arXiv 1212.1834 (2012).

  10. Spans of special cycles of codimension less than 5.
    J. Reine Angew. Math. 718 (2016), pp. 39–57. and arXiv 1302.1451 (2013).

  11. Sturm Bounds for Siegel Modular Forms.
    Joint with Olav Richter.
    Res. in Number Theory (2015) 1.5 and arXiv 1501.07733 (2015).

  12. Kudla’s Modularity Conjecture and Formal Fourier-Jacobi Series.
    Joint with Jan Hendrik Bruinier.
    Forum Math. Pi 3 (2015), 30 pp. and arXiv 1409.4996 (2014).

  13. Formal Fourier Jacobi Expansions and Special Cycles of Codimension Two.
    Compos. Math. 151.12 (2015) pp. 2187-2211 and arXiv 1302.0880 (2013).

  14. The Structure of Siegel Modular Forms modulo p and U(p) Congruences.
    Joint with Olav Richter.
    Math. Res. Lett. 22.3 (2015), pp. 899-928 and arXiv 1312.559 (2013).

  15. Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition.
    Joint with Kathrin Bringmann and Olav Richter.
    Trans. Amer. Math. Soc. 367.9 (2015), pp. 6647-6670 and arXiv 1207.5600 (2012).

  16. H-harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Some Indefinite Theta Series.
    Res. Math. Sci. (2015) 2.12 and arXiv 1207.5603 (2012).

  17. Holomorphic projections and Ramanujan’s mock theta functions.
    Joint with Ozlem Imamoglu and Olav Richter.
    Proc. Nat. Acad. Sci. U.S.A. 111.11 (2014), pp. 3961-3967 and arXiv 1306.3919 (2013).

  18. M24-twisted Product Expansions are Siegel Modular Forms.
    Commun. Number Theory Phys. 7.3 (2013) and arXiv 1208.3453 (2012).

  19. Mock period functions, sesquiharmonic Maass forms, and non-critical values of L-functions.
    Joint with Kathrin Bringmann and Nikolaus Diamantis.
    Advances in Math. 233 (2013), pp. 115-134 and arXiv 1107.0573 (2011).

  20. Computing Borcherds Products.
    Joint with Dominic Gehre and Judith Kreuzer.
    LMS J. Comput. Math. 16 (2013), pp. 200-215 and arXiv 1111.5574 (2011).

  21. The functional equation of the twisted spinor L-function in genus 2.
    Joint with Aloys Krieg.
    Abh. Math. Semin. Univ. Hambg. 83.1 (2013), pp. 29-52 and arXiv 0907.2767 (2009).

  22. Kohnen’s limit process for real-analytic Siegel modular forms.
    Joint with Kathrin Bringmann and Olav Richter.
    Advances in Math. 231 (2012), pp. 1100-1118 and arXiv 1105.5482 (2011).

  23. How to implement a modular form.
    J. Symb. Comp. 46.12 (2011), pp. 1336-1354 and MPI Preprint 582312 (2010).

  24. Hecke algebras related to the unimodular and modular groups over quadratic field extensions and quaternion algebras.
    Proc. Amer. Math. Soc. 139.4 (2011), pp. 1321-1331 and arXiv 0907.2766 (2009).

  25. Efficiently generated spaces of classical Siegel modular forms and the Boecherer conjecture.
    J. Aust. Math. Soc. 89.3 (2010), pp. 393-405 and arXiv 1002.3883 (2010).

Accepted

Preprints

Books

Various Publications

Software

Preprints no longer intended for publication

Advising

PostDocs

PhD Students

Teaching

I teach a course on High Performance Computing (TMA881, MMA620) during the 1st term 2020/21.

Given Courses

Downloads

Contact

My office is

My post address is

You can send me mail at raum@chalmers.se.