An Introduction to the Smarandache Function
by Charles Ashbacher
Publisher: Erhus Univ Pr 1995
Number of pages: 62
As one of the oldest mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve, which is the origin of their charm. All mathematicians have a soft spot in their hearts for the "purity" of the integers. In the 1970's a Rumanian mathematician Florentin Smarandache created a new function in number theory. The consequences of its simple definition encompass many areas of mathematics. The purpose of this text is to examine some of those consequences, giving the reader a taste for this unexplored territory.
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by Douglas Ulmer - arXiv
The focus is on elliptic curves over function fields over finite fields. We explain the main classical results on the Birch and Swinnerton-Dyer conjecture in this context and its connection to the Tate conjecture about divisors on surfaces.
by Felice Russo - American Research Press
The fascinating Smarandache's universe is halfway between the recreational mathematics and the number theory. This book presents new Smarandache functions, conjectures, solved and unsolved problems, new type sequences and new notions in number theory.
by Pete L. Clark - University of Georgia
The goal is to find and explore open questions in both geometry of numbers -- e.g. Lattice Point Enumerators, the Ehrhart-Polynomial, Minkowski's Convex Body Theorems, Minkowski-Hlawka Theorem, ... -- and its applications to number theory.
by Wolfgang M. Schmidt - Tata Institute of Fundamental Research
The theory of Irregularities of Distribution began as a branch of Uniform Distributions, but is of independent interest. In these lectures the author restricted himself to distribution problems with a geometric interpretation.