Jan Hendrik Bruinier

Technical University of Darmstadt

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Druck Stückle

Paderborn University

Franz Printing

Tbilisi State University

Christopher Lafayette

Japan Science and Technology Agency

West Shahidi

Walter de Gruyter (Germany)

Frank Duzaar

University of Salzburg

Siegfried Echterhoff

Walter de Gruyter (Germany)

Jan Frahm

Aarhus University

Valentin Blomer

University of Bonn

Baltimore Sogge

Japan Science and Technology Agency

Fred Cohen

University of Rochester

Cooperative Institutions

Walter de Gruyter (Germany)

Technical University of Darmstadt

Japan Science and Technology Agency

Gunma Astronomical Observatory

Délégation Paris 6

Max Planck Institute for Mathematics

University of Göttingen

Heidelberg University

Max Planck Society

University of Bonn

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The 1-2-3 of modular forms: lectures at a summer school in Nordfjordeid, Norway

Choice Reviews Online (2009)

Jan Hendrik Bruinier

Elliptic Modular Forms and Their Applications.- Hilbert Modular Forms and Their Applications.- Siegel Modular Forms and Their Applications.- Congruence Between a Siegel and an Elliptic Modular Form.

10.5860/choice.46-3900

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Citations (199)

References

Lecture notes in mathematics (2002)

Jan Hendrik Bruinier

10.1007/978-3-540-45872-2_7

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The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004.

Jan Hendrik Bruinier Gerard van der Geer Günter Harder Don Zagier

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Frontmatter

Forum Mathematicum (2021)

Jan Hendrik Bruinier Darmstadt Editorial Board Valentin Blomer Fred Cohen Rochester Droste

10.1515/forum-2021-frontmatter4

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Frontmatter

Forum Mathematicum (2019)

Jan Hendrik Bruinier Jörg Brüdern Frederick Göttingen Rochester Cohen Manfred Montreal

10.1515/forum-2019-frontmatter3

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Forum Mathematicum (1996)

Jan Hendrik Bruinier Darmstadt Editorial Board Valentin Blomer Fred Cohen Rochester Droste

Rudnick and Wigman (2008) conjectured that the variance of the volume of the nodal set of arithmetic random waves on the d -dimensional torus is O⁢(E/𝒩){O(E/\mathcal{N})}, as E→∞{E\to\infty}, where E is the energy and 𝒩{\mathcal{N}} is the dimension of the eigenspace corresponding to E . Previous results have established this with stronger asymptotics when d=2{d=2} and d=3{d=3}. In this brief note we prove an upper bound of the form O⁢(E/𝒩1+α⁢(d)-ϵ){O(E/\mathcal{N}^{1+\alpha(d)-\epsilon})}, for any ϵ>0{\epsilon>0} and d≥4{d\geq 4}, where α⁢(d){\alpha(d)} is positive and tends to zero with d . The power saving is the best possible with the current method (up to ϵ) when d≥5{d\geq 5} due to the proof of the ℓ2{\ell^{2}}-decoupling conjecture by Bourgain and Demeter.

Decoupling (probability)

Zero (linguistics)

10.1515/form.1996.issue-8

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5. Chern classes of Heegner divisors

Lecture notes in mathematics (2002)

Jan Hendrik Bruinier

Lift (data mining)

10.1007/978-3-540-45872-2_6

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Special cycles on toroidal compactifications of orthogonal Shimura varieties

Mathematische Annalen (2021)

Jan Hendrik Bruinier Shaul Zemel

Abstract We determine the behavior of automorphic Green functions along the boundary components of toroidal compactifications of orthogonal Shimura varieties. We use this analysis to define boundary components of special divisors and prove that the generating series of the resulting special divisors on a toroidal compactification is modular.

Shimura variety

Compactification (mathematics)

10.1007/s00208-021-02271-x

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Heights of Kudla–Rapoport divisors and derivatives of $$L$$ L -functions

Inventiones mathematicae (2014)

Jan Hendrik Bruinier Benjamin Howard Tonghai Yang

Shimura variety

Lift (data mining)

Cusp form

10.1007/s00222-014-0545-9

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Harmonic Maass forms and periods

arXiv (Cornell University) (2011)

Jan Hendrik Bruinier

According to Waldspurger's theorem, the coefficients of half-integral weight eigenforms are given by central critical values of twisted Hecke L-functions, and therefore by periods. Here we prove that the coefficients of weight 1/2 harmonic Maass forms are determined by periods of algebraic differentials of the third kind on modular and elliptic curves.

Harmonic

10.48550/arxiv.1111.1508

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