More Like this

1. On the nonexistence of automorphic eigenfunctions of exponential growth on SL(3,Z)∖SL(3,R)/SO(3,R)

   https://doi.org/10.1007/s40993-019-0168-8  

   Miller, Stephen D.; Trinh, Tien D. (October 2019, Research in number theory)

   It is well-known that there are automorphic eigenfunctions on SL(2,Z)∖SL(2,R)/SO(2,R)—such as the classical j-function—that have exponential growth and have exponentially growing Fourier coefficients (e.g., negative powers of q=e2πiz, or an I-Bessel function). We show that this phenomenon does not occur on the quotient SL(3,Z)∖SL(3,R)/SO(3,R) and eigenvalues in general position (a removable technical assumption). More precisely, if such an automorphic eigenfunction has at most exponential growth, it cannot have non-decaying Whittaker functions in its Fourier expansion. This confirms part of a conjecture of Miatello and Wallach, who assert all automorphic eigenfunctions on this quotient (among other rank ≥2 examples) always have moderate growth. We additionally confirm their conjecture under certain natural hypotheses, such as the absolute convergence of the eigenfunction’s Fourier expansion. 

   more » « less
2. Crystallization Retardation of Ultrathin Films of Poly[(R)-3-hydroxybutyrate] and a Random Copolymer Poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate] on an Aluminum Oxide Surface,

   https://doi.org/10.1021/acs.macromol.9b01214  

   Liu, Changhao; Noda, Isao; Chase, D. Bruce; Zhang, Yuying; Qu, Jing; Jia, Meng; Ni, Chaoying; Rabolt, John F. (January 2019, Macromolecules)

   null (Ed.)
3. Legendrian contact homology in $$\mathbb{R}^3$$

   https://doi.org/10.4310/SDG.2020.v25.n1.a4  

   Etnyre, John B.; Ng, Lenhard L. (January 2020, Surveys in Differential Geometry)
4. Packing Nearly Optimal Ramsey R(3,t) Graphs

   https://doi.org/10.1007/s00493-019-3921-7  

   Guo, He; Warnke, Lutz (February 2020, Combinatorica)

   null (Ed.)
5. Polymorphic Distribution in Individual Electrospun Poly[( R )-3-hydroxybutyrate- co -( R )-3-hydroxyhexanoate] (PHBHx) Nanofibers

   https://doi.org/10.1021/acs.macromol.7b01086  

   Gong, Liang; Chase, D. Bruce; Noda, Isao; Marcott, Curtis A.; Liu, Jinglin; Martin, David C.; Ni, Chaoying; Rabolt, John F. (July 2017, Macromolecules)