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Relevant bibliographies by topics / Hilbert modular surfaces

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Journal articles

Academic literature on the topic 'Hilbert modular surfaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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Journal articles on the topic "Hilbert modular surfaces"

1

McREYNOLDS, D. B. "Cusps of Hilbert modular varieties." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (2008): 749–59. http://dx.doi.org/10.1017/s0305004107001004.

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AbstractMotivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifoldMto be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3–manifold is diffeo morphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3–manifolds that cannot arise as a cusp cross-section of a 1–cusped n

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2

Faltings, Gerd. "Book Review: Hilbert modular surfaces." Bulletin of the American Mathematical Society 20, no. 2 (1989): 247–52. http://dx.doi.org/10.1090/s0273-0979-1989-15783-2.

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3

McMullen, Curtis T. "Foliations of Hilbert modular surfaces." American Journal of Mathematics 129, no. 1 (2007): 183–215. http://dx.doi.org/10.1353/ajm.2007.0002.

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4

Milio, Enea, and Damien Robert. "Modular polynomials on Hilbert surfaces." Journal of Number Theory 216 (November 2020): 403–59. http://dx.doi.org/10.1016/j.jnt.2020.04.014.

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5

Hamahata, Yoshinori. "Hilbert Modular Surfaces withpg ≤ 1." Mathematische Nachrichten 173, no. 1 (1995): 193–236. http://dx.doi.org/10.1002/mana.19951730113.

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6

Elkies, Noam, and Abhinav Kumar. "K3 surfaces and equations for Hilbert modular surfaces." Algebra & Number Theory 8, no. 10 (2014): 2297–411. http://dx.doi.org/10.2140/ant.2014.8.2297.

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7

Möller, Martin, and Don Zagier. "Modular embeddings of Teichmüller curves." Compositio Mathematica 152, no. 11 (2016): 2269–349. http://dx.doi.org/10.1112/s0010437x16007636.

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Fuchsian groups with a modular embedding have the richest arithmetic properties among non-arithmetic Fuchsian groups. But they are very rare, all known examples being related either to triangle groups or to Teichmüller curves. In Part I of this paper we study the arithmetic properties of the modular embedding and develop from scratch a theory of twisted modular forms for Fuchsian groups with a modular embedding, proving dimension formulas, coefficient growth estimates and differential equations. In Part II we provide a modular proof for an Apéry-like integrality statement for solutions of Pica

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8

Kumar, Abhinav, and Ronen E. Mukamel. "Real multiplication through explicit correspondences." LMS Journal of Computation and Mathematics 19, A (2016): 29–42. http://dx.doi.org/10.1112/s1461157016000188.

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We compute equations for real multiplication on the divisor classes of genus-2 curves via algebraic correspondences. We do so by implementing van Wamelen’s method for computing equations for endomorphisms of Jacobians on examples drawn from the algebraic models for Hilbert modular surfaces computed by Elkies and Kumar. We also compute a correspondence over the universal family for the Hilbert modular surface of discriminant $5$ and use our equations to prove a conjecture of A. Wright on dynamics over the moduli space of Riemann surfaces.

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9

Gon, Yasuro. "Determinants of Laplacians on Hilbert modular surfaces." Publicacions Matemàtiques 62 (July 1, 2018): 615–39. http://dx.doi.org/10.5565/publmat6221808.

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10

EHLEN, STEPHAN. "TWISTED BORCHERDS PRODUCTS ON HILBERT MODULAR SURFACES AND THE REGULARIZED THETA LIFT." International Journal of Number Theory 06, no. 07 (2010): 1473–89. http://dx.doi.org/10.1142/s1793042110003642.

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We construct a lifting from weakly holomorphic modular forms of weight 0 for SL 2(ℤ) with integral Fourier coefficients to meromorphic Hilbert modular forms of weight 0 for the full Hilbert modular group of a real quadratic number field with an infinite product expansion and a divisor given by a linear combination of twisted Hirzebruch–Zagier divisors. The construction uses the singular theta lifting by considering a suitable twist of a Siegel theta function. We generalize the work by Bruinier and Yang who showed the existence of the lifting for prime discriminants using a different approach.

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