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Möbius, Mellin, and mathematical physics

Author

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  • Ninham, Barry W.
  • Hughes, Barry D.
  • Frankel, Norman E.
  • Lawrence Glasser, M.

Abstract

We examine some results and techniques of analytic number theory which have application, or potential application, in mathematical physics. We consider inversion formulae for lattice sums, various transformations of infinite series and products, functional equations and scaling relations, with selected applications in electrostatics and statistical mechanics. In the analysis, the Mellin transform and the Riemann zeta function play a key role.

Suggested Citation

  • Ninham, Barry W. & Hughes, Barry D. & Frankel, Norman E. & Lawrence Glasser, M., 1992. "Möbius, Mellin, and mathematical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 186(3), pages 441-481.
    • Handle: RePEc:eee:phsmap:v:186:y:1992:i:3:p:441-481
    DOI: 10.1016/0378-4371(92)90210-H
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    Cited by:

    1. Planat, Michel, 2003. "Thermal 1/f noise from the theory of partitions: application to a quartz resonator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 371-386.

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