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The evaluation of two-dimensional lattice sums via Ramanujan's theta functions

Volume 165 / 2014

Ping Xu Acta Arithmetica 165 (2014), 57-89 MSC: Primary 33E05; Secondary 11F27, 35J05. DOI: 10.4064/aa165-1-4

Abstract

We analyze various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many explicit examples are given.

Authors

  • Ping XuDepartment of Mathematics
    University of Illinois at Urbana-Champaign
    1409 W. Green Street
    Urbana, IL 61801, U.S.A.
    and
    439 Cambridge St. Apt 23
    Allston, MA 02134, U.S.A.
    e-mail

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