2013/12/04 by Atul Dixit, Dixit, Atul, Victor H. Moll +1
Mathematics · Physics and Astronomy · #11M06 #33C05 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #math-ph #math.MP #math.NT #msc:11M06 #msc:33C05
paper · pdf · doi:10.48550/arxiv.1312.1232
34 pages; submitted for publication
arxiv created 2013/12/04 · arxiv updated 2013/12/05
The classical transformation of Jacobi's theta function admits a simple proof by producing an integral representation that yields this invariance apparent. This idea seems to have first appeared in the work of S. Ramanujan. Several examples of this idea have been produced by Koshlyakov, Ferrar, Guinand, Ramanujan and others. A unifying procedure to analyze these examples and natural generalizations is presented.