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 C. Dumitrescu, V. Seleacu - Erhus University Press
The function in the title is originated from the Romanian mathematician Florentin Smarandache, who has significant contributions in mathematics and literature. This text introduces the Smarandache function and discusses its generalisations.
by J.S. Milne
This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms. Because of their brevity, many proofs have been omitted or only sketched.
by Jozsef Sandor - American Research Press
Contents: on Smarandache's Podaire theorem, Diophantine equation, the least common multiple of the first positive integers, limits related to prime numbers, a generalized bisector theorem, values of arithmetical functions and factorials, and more.
by Steve Wright - arXiv
Beginning with Gauss, the study of quadratic residues and nonresidues has subsequently led directly to many of the ideas and techniques that are used everywhere in number theory today, and the primary goal of these lectures is to use this study ...