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This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois …
Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting …
The Waring-Goldbach problem seeks to represent positive integers satisfying necessary congruence conditions by powers of primes. The circle method of Hardy and Littlewood in …
In the late 1970s, using higher algebraic K-theory, class field theory was generalized to higher-dimensional local and global fields. Thus, it is a very natural question to ask and …
This monograph elucidates and extends many theorems and conjectures in analytic number theory and algebraic asymptotic analysis via the natural notions of degree and logexponential …