Papers and Preprints

Preprints

An explicit refined Gan-Gross-Prasad identity for Fourier-Jacobi periods of degree 2 Siegel cusp forms (with B. Paul, A. Pitale and R. Schmidt)

Publications

The pdf files below correspond to the "postprint" (final accepted version). To access the final published version, click the DOI links.

Simple supercuspidal representations of GSp₄ and test vectors (with A. Pitale and R. Schmidt)
Math. Z. (2026), 314(8). DOI: 10.1007/s00209-026-04101-9

Bounds on Fourier coefficients and global sup-norms for Siegel cusp forms of degree 2 (with F. Comtat and J. Marzec-Ballesteros)
J. Lond. Math. Soc. (2025), 111:3. DOI: 10.1112/jlms.70119

Mass equidistribution for Saito-Kurokawa lifts (with J. Jääsaari and S. Lester)
Geom. Funct. Anal. (GAFA) (2024), 34: 1460-1532. DOI: 10.1007/s00039-024-00690-x

The Manin constant and the modular degree (with K. Česnavičius and M. Neururer)
J. Eur. Math. Soc. (JEMS) (2024), 2: 573-637. DOI: 10.4171/JEMS/1367

On Fourier coefficients and Hecke eigenvalues of Siegel cusp forms of degree 2 (with B. Paul)
Int. Math. Res. Not. (IMRN) (2023), 24: 21707-21760. DOI: 10.1093/imrn/rnac316

The special values of the standard L-functions for GSp_2n × GL₁ (with S. Horinaga, A. Pitale and R. Schmidt)
Trans. Amer. Math. Soc., (2022), 375: 6947-6982. DOI: 10.1090/tran/8617

On fundamental Fourier coefficients of Siegel cusp forms of degree 2 (with J. Jääsaari and S. Lester)
J. Inst. Math. Jussieu (2021), 22(4): 1819-1869. DOI: 10.1017/S1474748021000542

Integrality and cuspidality of pullbacks of nearly holomorphic Siegel Eisenstein series (with A. Pitale and R. Schmidt)
Publicacions Matemàtiques (2022), 66(1): 405-434. DOI: 10.5565/PUBLMAT6612216

Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, II: newforms and subconvexity (with Y. Hu)
Compositio Math. (2020), 156(11): 2368-2398. DOI: 10.1112/S0010437X20007460

On the standard L-function for GSp_2n × GL₁ and algebraicity of symmetric fourth L-values for GL₂ (with A. Pitale and R. Schmidt)
Ann. Math. Québec. (2021), 45: 113-159. DOI: 10.1007/s40316-020-00134-6.

Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces
Math. Ann. (2020), 376(1): 609-644. DOI: 10.1007/s00208-019-01923-3.

Explicit refinements of Böcherer's conjecture for Siegel modular forms of squarefree level (with M. Dickson, A. Pitale and R. Schmidt)
J. Math. Soc. Japan. (2020), 72(1): 251-301. DOI: 10.2969/jmsj/78657865.

Lowest weight modules of Sp₄(R) and nearly holomorphic Siegel modular forms (with A. Pitale and R. Schmidt)
Kyoto J. Math. (2021), 61(4): 745-814. DOI: 10.1215/21562261-2021-0012.

Some analytic aspects of automorphic forms on GL(2) of minimal type (with P. Nelson and Y. Hu)
Comm. Math. Helv. (2019), 94(4): 767-801. DOI: 10.4171/CMH/473.

On the order of vanishing of newforms at cusps (with A. Corbett)
Math. Res. Lett. (2018), 25(6): 1771-1804. DOI: 10.4310/MRL.2018.v25.n6.a4.

A note on the growth of nearly holomorphic vector-valued Siegel modular forms (with A. Pitale and R. Schmidt)
L-functions and automorphic forms, Contrib. Math. Comput. Sci. (2018), 10. DOI:10.1007/978-3-319-69712-3.

Hybrid sup-norm bounds for Maass newforms of powerful level
Algebra and Number Theory (2017), 11(5): 1009-1045. DOI: 10.2140/ant.2017.11.1009.

On sup-norms of cusp forms of powerful level
J. Eur. Math. Soc. (JEMS) (2017), 19(11):3549-3573. DOI: 10.4171/JEMS/746.

Local and global Maass relations (with A. Pitale and R. Schmidt)
Math. Z. (2017), 287(1-2):655-677. DOI:10.1007/s00209-016-1840-5.
Download a longer version which gives more computational details:

Representations of SL₂(R) and nearly holomorphic modular forms (with A. Pitale and R. Schmidt)
RIMS Kokyyroku (2016), 1973: 141-153.

Large values of newforms on GL(2) with highly ramified central character
Int. Math. Res. Not. (IMRN) (2016), 2016(13): 4103-4131. DOI: 10.1093/imrn/rnv259.

On ratios of Petersson norms for Yoshida lifts
Forum Mathematicum (2015), 27(4): 2361-2412. DOI: 10.1515/forum-2013-0093.

Transfer of Siegel cusp forms of degree 2 (with A. Pitale and R. Schmidt)
Mem. Amer. Math. Soc. (2014), 232 (1090). DOI:10.1090/memo/1090.

Bounds for Rankin-Selberg integrals and quantum unique ergodicity for powerful levels (with P. Nelson and A. Pitale)
J. Amer. Math. Soc. (2014), 27: 147-191. DOI:10.1090/S0894-0347-2013-00779-1.

A relation between multiplicity one and Böcherer's conjecture
Ramanujan J. (2014), 33(2): 263-268. DOI:10.1007/s11139-013-9489-8.

Yoshida lifts and simultaneous non-vanishing of dihedral twists of modular L-functions (with R. Schmidt)
J. Lond. Math. Soc. (2013), 88 (1): 251-270. DOI:10.1112/jlms/jdt008.

Determination of modular forms by fundamental Fourier coefficients
Automorphic Representations and L-Functions (2013), Proceedings of the International Colloquium on Automorphic Representations and L-Functions (TIFR, Mumbai, India).

Siegel cusp forms of degree 2 are determined by their fundamental Fourier coefficients
Math. Ann. (2013), 355(1):363--380. DOI:10.1007/s00208-012-0789-x

Local spectral equidistribution for Siegel modular forms and applications (with E. Kowalski and J. Tsimerman)
Compositio Math. (2012), 148(2):335--384. DOI:10.1112/S0010437X11007391

Prime density results for Hecke eigenvalues of a Siegel cusp form
Int. J. Number Theory (2011), 7(4):971--979. DOI:10.1142/S1793042111004642

A note on Fourier coefficients of Poincaré series (with E. Kowalski and J. Tsimerman)
Mathematika (2011), 57(1):31--40. DOI:10.1112/S0025579310001804

Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) × GL(2)
Pacific J. Math. (2010), 246(2):435--486. DOI:10.2140/pjm.2010.246.435

L-functions for holomorphic forms on GSp(4) × GL(2) and their special values
Int. Math. Res. Not. (IMRN) (2009), 2009(10):1773--1837. DOI:10.1093/imrn/rnp001
Download an unedited version which gives more computational details:

Hilbert modular forms of weight 1/2 and theta functions (with S. Achimescu)
J. Number Theory (2008), 128(12):3037--3062. DOI:10.1016/j.jnt.2008.04.001

Ph.D. Thesis

On critical values of L-functions for holomorphic forms on GSp(4) × GL(2)
California Institute of Technology, Dissertation (149 pages), 2009.

Expository mathematics articles

Sums of powers of the primitive roots of a prime
Resonance, 7(2):86--89, 2002.

Selected talk Slides

A 60-minute talk on mass equidistibution for Saito-Kurokawa lifts, given at the University of Oxford, 2023

A 60-minute talk on the Manin constant and Fourier expansions at cusps, given at the University of Nottingham, 2022

A 20-minute talk on critical values and algebraicity, given at AFW 2018

A 60-minute colloquium style talk on some analytic aspects of automorphic forms, given at the University of Oklahoma, 2018

A 60-minute talk on sup-norms for newforms of powerful level, given at Copenhagen, 2016

A 60-minute survey talk on Siegel cusp forms of degree 2 that I gave at Sheffield in 2014.

A 45-minute talk at the BMC 2014, focussing on nearly holomorphic modular forms of degree 2.

A 60-minute talk on non-vanishing of fundamental Fourier coefficients and applications, given at TIFR in 2012.

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