An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook

• Autores: Bruce C. Berndt, Ping Xu
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 147, Nº 2, 2009, págs. 257-265
• Idioma: inglés
• DOI: 10.1017/s0305004109002552
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• Resumen

  • One page in Ramanujan's lost notebook is devoted to claims about a certain integral with two parameters. One claim gives an inversion formula for the integral that is similar to the transformation formula for theta functions. Other claims are remindful of Gauss sums. In this paper we prove all the claims made by Ramanujan about this integral.