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J. Voight (2006)
Shimura curve computations
R. Borcherds (1996)
Automorphic forms with singularities on GrassmanniansInventiones mathematicae, 132
P. Griffiths (1989)
Introduction to Algebraic Curves
B. Gross, D. Zagier (1986)
Heegner points and derivatives ofL-seriesInventiones mathematicae, 84
Claudia Alfes, Stephan Ehlen (2011)
Twisted traces of CM values of weak Maass formsJournal of Number Theory, 133
G. Shimura (1973)
Modular Forms of Half Integral Weight
SP Zwegers (2001)
Mock $$\theta $$ θ -Functions and Real Analytic Modular Forms, $$q$$ q -Series with Applications to Combinatorics, Number Theory, and Physics (Urbana, IL, 2000). Contemporary Mathematics
J. Bruinier, Jens Funke (2004)
Traces of CM values of modular functions, 2006
Jens Funke, J. Millson (2001)
Cycles in hyperbolic manifolds of non-compact type and Fourier coefficients of Siegel modular formsmanuscripta mathematica, 107
Marina Daecher (2016)
Introduction To Cyclotomic Fields
(1982)
Geodesic cyclics and the Weil representation . I . Quotients of hyperbolic space and Siegel modular forms
S. Zwegers (2008)
Mock Theta FunctionsarXiv: Number Theory
B Gross, W Kohnen, D Zagier (1987)
Heegner points and derivatives of $$L$$ L -series. IIMath. Ann., 278
Jens Funke (2002)
Heegner Divisors and Nonholomorphic Modular FormsCompositio Mathematica, 133
G. Wüstholz (1984)
Zum PeriodenproblemInventiones mathematicae, 78
A. Scholl (1986)
Fourier coefficients of Eisenstein series on non-congruence subgroupsMathematical Proceedings of the Cambridge Philosophical Society, 99
J Voight (2009)
Shimura Curve Computations. Arithmetic Geometry, Clay Mathematics Proceedings
LC Washington (1997)
Introduction to Cyclotomic Fields. Graduate Texts in Mathematics
A. Dabholkar, S. Murthy, D. Zagier (2012)
Quantum Black Holes, Wall Crossing, and Mock Modular FormsarXiv: High Energy Physics - Theory
Friedrich Hirzebruch, Don Zagier (1976)
Intersection numbers of curves on Hilbert modular surfaces and modular forms of NebentypusInventiones Mathematicae, 36
S. Zwegers (2008)
MOCK θ-FUNCTIONS AND REAL ANALYTIC MODULAR
J Bruinier, K Ono (2010)
Heegner divisors, $$L$$ L -functions and harmonic weak Maass formsAnn. Math. (2), 172
J. Bruinier, Jens Funke (2002)
On two geometric theta liftsDuke Mathematical Journal, 125
N. Skoruppa (1990)
Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular formsInventiones mathematicae, 102
SS Kudla, JJ Millson (1990)
Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variablesInst. Hautes Études Sci. Publ. Math., 71
Victoria Powers (2018)
SOCIÉTÉ MATHÉMATIQUE DE FRANCE
Jens Funke, S. Kudla (2017)
Mock modular forms and geometric theta functions for indefinite quadratic formsJournal of Physics A: Mathematical and Theoretical, 50
S. Kudla, J. Millson (1990)
Intersection numbers of cycles on locally symmetric spaces and fourier coefficients of holomorphic modular forms in several complex variablesPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 71
J. Bruinier, Markus Schwagenscheidt (2016)
Algebraic formulas for the coefficients of mock theta functions and Weyl vectors of Borcherds productsJournal of Algebra, 478
J. Bruinier, K. Ono (2007)
Heegner divisors, $L$-functions and harmonic weak Maass formsarXiv: Number Theory
M. Waldschmidt, D. Bertrand, J. Serre (1987)
Nombres transcendants et groupes algébriques
S. Kudla (2016)
Theta integrals and generalized error functionsmanuscripta mathematica, 155
T. Shintani (1975)
On construction of holomorphic cusp forms of half integral weightNagoya Mathematical Journal, 58
D. Zagier (2009)
Ramanujan's mock theta functions and their applications (after Zwegers and Ono-Bringmann)
S. Kudla, J. Millson (1986)
The theta correspondence and harmonic forms. IMathematische Annalen, 274
The Shimura correspondence connects modular forms of integral weights and half-integral weights. One of the directions is realized by the Shintani lift, where the inputs are holomorphic differentials and the outputs are holomorphic modular forms of half-integral weight. In this article, we generalize this lift to differentials of the third kind. As an application, we obtain a modularity result concerning the generating series of winding numbers of closed geodesics on the modular curve.
Research in the Mathematical Sciences – Springer Journals
Published: Apr 30, 2018
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