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We give a unified description of the modular and quasi-modular functions used in Viazovska's proof of the best packing bounds in dimension 8 and the proof by Cohn, Kumar, Miller, Radchenko, and Viazovska of the best packing bound in dimension 24.
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J. H. Bruinier, G. van der Geer, G. Harder, and D. Zagier, The 1-2-3 of modular forms , Universitext, Springer-Verlag, Berlin, 2008, Lectures from the Summer School on Modular Forms and their Applications held in Nordfjordeid, June 2004, Edited by Kristian Ranestad
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H. Cohen and F. Strömberg, Modular forms , Graduate Studies in Mathematics, vol. 179, American Mathematical Society, Providence, RI, 2017, A classical approach
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by same author, A conceptual breakthrough in sphere packing , Notices Amer. Math. Soc. 64
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H. Cohn, A. Kumar, S. D. Miller, D. Radchenko, and M. Viazovska, The sphere packing problem in dimension 24 , Ann. of Math. (2) 185
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F. Gonçalves, D. Oliveira e Silva, and S. Steinerberger, Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots , J. Math. Anal. Appl. 451
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M. S. Viazovska, The sphere packing problem in dimension 8 , Ann. of Math. (2) 185
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Y. J. Choie and M. H. Lee, Jacobi-Like Forms, Pseudodifferential Operators, and Quasimodular Forms , Monographs in Mathematics, Springer International Publishing, 2019
2019
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H. Cohn and F. Gonçalves, An optimal uncertainty principle in twelve dimensions via modular forms , Invent. Math. 217
2019
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2019
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D. Radchenko and M. Viazovska, Fourier interpolation on the real line , Publ. Math. Inst. Hautes Études Sci. 129
2019
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L. Rolen and I. Wagner, A note on Schwartz functions and modular forms , Arch. Math. (2020), to appear
2020
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