[2] **viXra:1109.0054 [pdf]**
*submitted on 27 Sep 2011*

**Authors:** Ranganath G Kulkarni

**Comments:** 3 pages

Mathematical constant e can be expressed in logarithmic functions. There are six expressions
for e. Five of them are step functions and another one is a constant function.

**Category:** Number Theory

[1] **viXra:1109.0029 [pdf]**
*submitted on 9 Sep 2011*

**Authors:** Huaning Liu, Jing Gao

**Comments:** 155 pages

This book systematically introduces the works obtained by using analytic methods on
Smarandache problems. The book includes the basic knowledge of analytic number theory, mean
value on some Smarandache sequences, infinite series involving some Smarandache functions,
hybrid mean value of divisor function and some Smarandache functions, and so on. This book
could open up the reader's perspective, and inspire the reader to these fields.
We want to thank all those who have helped and encouraged us to prepare this book. Professor
Wenpeng Zhang gave us the first impulse for writing this book, and have read the whole manuscript
very carefully. We also thank Yanni Liu and Peng Gao for cover designs. Last but not least,
we would like to thank Dr. Minh Perez for his advice and friendly collaboration.

**Category:** Number Theory