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Maximal theta functions universal optimality of the hexagonal lattice for Madelung-like lattice energies

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  • معلومة اضافية
    • Contributors:
      Institut Camille Jordan (ICJ); École Centrale de Lyon (ECL); Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL); Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS); Équations aux dérivées partielles, analyse (EDPA); Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL); University of Vienna Vienna
    • بيانات النشر:
      HAL CCSD
      Springer
    • الموضوع:
      2023
    • نبذة مختصرة :
      International audience ; We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H. Montgomery, Minimal theta functions. Glasgow Mathematical Journal, 30 (1988), 75–85]. The studied theta functions are generalizations of the Jacobi theta-2 and theta-4 functions. Contrary to Montgomery’s result, we show that, among lattices, the hexagonal lattice is the unique maximizer of both families of theta functions. As an immediate consequence, we obtain a new universal optimality result for the hexagonal lattice among two-dimensional alternating charged lattices and lattices shifted by the center of their unit cell.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2007.15977; hal-04454233; https://hal.science/hal-04454233; https://hal.science/hal-04454233/document; https://hal.science/hal-04454233/file/maxtheta_charge.pdf; ARXIV: 2007.15977
    • الرقم المعرف:
      10.1007/s11854-022-0254-z
    • Rights:
      http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.AF26B0F3