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Ramanujan’s Notebooks: Part V
Gauss and Jacobi sums
Gauss Sums. Jacobi Sums and Cyclotomic Numbers. Evaluation of Jacobi Sums Over Fp. Determination of Gauss Sums Over Fp. Difference Sets. Jacobsthal Sums Over Fp. Residuacity. Reciprocity Laws.Expand
Ramanujan's Lost Notebook: Part I
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, AndrewsExpand
Ramanujan's Notebooks
During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. UponExpand
Number theory in the spirit of Ramanujan
Introduction Congruences for $p(n)$ and $\tau(n)$ Sums of squares and sums of triangular numbers Eisenstein series The connection between hypergeometric functions and theta functions Applications ofExpand
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
In [6], the author proved a transformation formula for a fairly broad class of analytic Eisenstein series. This transformation formula is easily converted into a transformation formula for a largeExpand
Ramanujan’s Theories of Elliptic Functions to Alternative Bases
In his famous paper [3], [10, pp. 23–39], Ramanujan offers several beautiful series representations for 1/pi. He first states three formulas, one of which is $$ \frac{4}{\pi } =Expand