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

• Autorzy: Ping Xu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11F27: Theta series; Weil representation; theta correspondences
• 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
• 33E05: Elliptic functions and integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 165
• Numer: 1
• Strony: 57-89

Daty

wydano

2014

Twórcy

autor

Ping Xu

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

Identyfikatory

DOI

10.4064/aa165-1-4