Number Theory
Three joint papers with Frobenius deal with the theory of elliptic functions. Today Stickelberger's name is most closely associated with his 1890 paper that established the Stickelberger relation for cyclotomic Gaussian sums. This generalized earlier work of Jacobi and Kummer and was later used by Hilbert in his formulation of the reciprocity laws in algebraic number fields. The Stickelberger relation also yields information about the structure of the class group of a cyclotomic field as a module over its abelian Galois group (cf Iwasawa theory).
Read more about this topic: Ludwig Stickelberger, Mathematical Contributions
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