By Ranjan Roy

This thorough paintings offers the elemental result of modular functionality idea as constructed throughout the 19th and early-twentieth centuries. It positive aspects attractive formulation and derives them utilizing skillful and creative manipulations, specially classical equipment usually missed this day. beginning with the paintings of Gauss, Abel, and Jacobi, the publication then discusses the test via Dedekind to build a idea of modular services autonomous of elliptic capabilities. The latter a part of the publication explains how Hurwitz accomplished this job and contains one among Hurwitz's landmark papers, translated by way of the writer, and delves into the paintings of Ramanujan, Mordell, and Hecke. For graduate scholars and specialists in modular varieties, this booklet demonstrates the relevance of those unique resources and thereby offers the reader with new insights into modern paintings during this area.

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