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. Upon… Expand

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, Andrews… Expand

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

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 large… Expand

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 of… Expand

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