I am Martin Westerholt-Raum, Associate Professor at Chalmers Technical University in Gothenburg, Sweden. Starting January 2016 I hold a Ungar Forskare grant by Vetenskapsrådet. From 2012 to 2014, I held an ETH Postdoctoral Fellowship, which was cofinanced by the Marie Curie Actions for People COFUND Program. I am former PhD student of Don B. Zagier at MPI for Mathematics in Bonn.

- Have a look at my CV.
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My major research interests are modular forms and their applications in mathematics and physics. More specifically, I am interested in

- Applications of autormorphic forms
- Cohomological automorphic forms and their extensions
- Siegel and orthogonal modular forms
- Explicit methods for autormorphic forms

- 2016 to 2020: Ungar Forskare, Vetenskapsrådet. 3,000,000 SEK.
- 2012 to 2014: ETH Fellowship, ETH Zürich and Marie-Curie COFUND Program. CHF 200,000.

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

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 arXiv version.

**Products of Vector Valued Eisenstein Series.**Forum Math. Ahead of print and arXiv 1411.3877 (2014).**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).**Sturm Bounds for Siegel Modular Forms.***Joint with Olav Richter.*Research in Number Theory (2015) 1.5 and arXiv 1501.07733 (2015).**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).**Formal Fourier Jacobi Expansions and Special Cycles of Codimension 2.**Compos. Math. 151.12 (2015) pp. 2187-2211 and arXiv 1302.0880 (2013).**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).**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).**H-harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Some Indefinite Theta Series.**Research in the Mathematical Sciences (2015) 2.12 and arXiv 1207.5603 (2012).**Computing Genus 1 Jacobi Forms.**Math. Comp. 85 (2016) pp. 931-960 and arXiv 1212.1834 (2012).**Spans of special cycles of codimension less than 5.**J. Reine Angew. Math. Ahead of print and arXiv 1302.1451 (2013).**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).**M24-twisted Product Expansions are Siegel Modular Forms.**Commun. Number Theory Phys. 7.3 (2013) and arXiv 1208.3453 (2012).**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).**Computing Borcherds Products.***Joint with Dominic Gehre and Judith Kreuzer.*LMS J. Comput. Math. 16 (2013), pp. 200-215 and arXiv 1111.5574 (2011).**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).**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).**How to implement a modular form.**J. Symb. Comp. 46.12 (2011), pp. 1336-1354 and MPI Preprint 582312 (2010).**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).**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).

**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.*Accepted for Commun. Number Theory Phys. 10.4 (2016). arXiv 1502.00557 (2015).**Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms.***Joint with Kathrin Bringmann and Olav Richter.*Accepted for Research in Mathematical Sciences. arXiv 1604.05105 (2016).

**Indefinite Theta Series on Tetrahedral Cones.**arXiv 1608.08874 (2016).**Hyper-Algebras of Vector-Values Modular Forms.**HAL-01289143 (2016).**HLinear: Exact Dense Linear Algebra in Haskell.***Joint with Alexandru Ghitza.*arXiv 1605.02532 (2016).**Harmonic Weak Siegel Maass Forms I.**arXiv 1510.03342 (2015).**Explicit computations of Siegel modular forms of degree two.***Joint with Nathan Ryan and Gonzalo Tornaría.*arXiv 1205.6255 (2012).**Elementary divisor theory for the modular group over quadratic field extensions and quaternion algebras.**arXiv 0907.2762 (2009).

**Siegel Modular Forms and Jacobi Forms.**In preparation. Publishing agreement with Springer.

**Harmonic weak Siegel Maass forms.**Oberwolfach Reports.**Analytic properties of some indefinite theta series.**Oberwolfach Reports 2016.3.**Appendix to Pinched hypersurfaces contract to round points by M. Franzen.**arXiv 1502.07908 (2015).**Symmetric Formal Fourier Jacobi Series and Kudla’s Conjecture.**Oberwolfach Reports 2014.2.**Dual weights in the theory of harmonic Siegel modular forms.**Ph.D. Thesis, University of Bonn (2012).**Konstanten der Arithmetik: Perioden und ihre Relationen.***Joint with Sven Raum.*Annual report of the Max Planck Society, MPI for Mathematics (2012).

**HLinear.**Github, https://github.com/martinra/hlinear (2015).**algebraic-structures.**Github, https://github.com/martinra/algebraic-structures (2015).**Contributions to Sage.**Sage Trac Server #19668, #14482, #13531, #11624, #11139, #10987, #10837, #8094, #7474, #6671, #6670, #6669, #5731, #4578..**Genus 1 Jacobi Forms.**Sage Trac Server #16448 (2014).**Computation Jacobi Forms.**Sage Extension in Purple Sage (2012).**Modular Forms Framework.**Sage Extension in Purple Sage (2011).**Computation of Siegel Modular Forms of Genus 2.***Joint with Alex Ghitza, Nathan Ryan, Nils-Peter Skoruppa, and Gonzalo Tornaría.*Sage Extension in Purple Sage (2011).

In the second period 2016/17, I teach a course on algebraic number theory. The course webpage will be available later.

In the fourth period 2015/16, I teach a course on high performance computing. See the course website for more information.

High Performance Computing. Lecture. Chalmers University of Technology, 2016, Summer Term.

Modular Forms and Generating Series. Lecture. Chalmers University of Technology, 2015, Winter Term.

Jacobi Forms: Applications and Computations. Lecture. ETH Zurich, 2013, Winter Term.

Sage and Quaternion Modular Forms. Project group. RWTH Aachen University, 2011, Summer Term.

Sage and Quaternion Modular Forms. Seminar. RWTH Aachen University, 2010, Winter Term.

Autormorphic Forms for GL(2). Seminar. RWTH Aachen University, 2010, Summer Term.

Elliptic Curves and Applications to Crytography. Seminar. RWTH Aachen University, 2009, Winter Term.

Algebraic Number Theory II. Lecture as teaching assistent. RWTH Aachen University, 2009, Summer Term.

Algebraic Number Theory II. Lecture as regular substitute lecturer. RWTH Aachen University, 2009, Summer Term.

Algebraic Number Theory I. Lecture as teaching assistent. RWTH Aachen University, 2008, Winter Term.

Jiacheng Xia Started 2016. Co-supervision with Dennis Eriksson. Chalmers University of Technology.

Andreas Freh Started 2012. Co-supervision with Aloys Krieg. RWTH Aachen University.

The Sage scripts used to compute Fourier expansions, and the resulting data.

The expansions of vector valued modular forms that I computed.

The Sage code used to compute the results, and the resuls in machine readable form.

A recent version of the modular forms framework, integrated into PSage, is available on GitHub. It does not, however, include all available implementations. I will integrate them into my PSage branch as soon as possible.

Example code and results that was used in this publication. Use my hermitian branch of Purple Sage.

Sage files containing the computer assisted proofs.

- Remark in Section 2.1
- Proof of Theorem 3, Equation (15)
- Proof of Theorem 3, T = 0
- Proof of Theorem 3, T has rank 2

My office is in

- Chalmers University of Technology
- Mathematics Department
- L2130
- Chalmers Tvärgata 3
- SE-412 96 Göteborg

My post address is

- Chalmers tekniska högskola
- Institutionen för Matematiska vetenskaper
- Martin Westerholt-Raum
- SE-412 96 Göteborg, Sweden

You can send me an e-mail at .