# Enrique Treviño

### Assistant Professor of Mathematics

#### Areas of Specialization

number theory, analytical and computational number theory

#### Education

PhD Dartmouth College 2011

Thesis: Numerically Explicit Estimates for Character Sums

Advisor: Carl Pomerance

MA Dartmouth College

BA University of Texas at El Paso

#### Selected Honors

Travel grant from the American Mathematical Society to attend the 1st Congress of the Americas held in Guanajuato in August 2013.

Swarthmore College Research Award (2011-2013)

GAANN Fellowship (2006-2007)

Top 200 in the 66th Putnam exam, Dec. 2005

#### Selected Courses Taught

MATH 330: Modern Algebra I

MATH 230: Abstract and Discrete Mathematics

MATH 160: Math Methods and Applications

MATH150: Introduction to Probability and Statistics

MATH 53 (Swarthmore College): Analytic Number Theory

MATH 77 (Swarthmore College): Algebraic Number Theory

MATH 27 (Swarthmore College): Honors Linear Algebra

MATH 25 (Swarthmore College): Calculus II

MATH 20 (Dartmouth College): Discrete Probability

#### Publications

#####
**Articles**

** The primes that Euclid forgot** (with P. Pollack), American Mathematical Monthly 121 (2014), no. 5, 433-437.

**Sets of monotonicity for Euler’s totient function**(with P. Pollack and C. Pomerance), The Ramanujan Journal 30 (2013), no. 3, 379-398.

**On the maximum number of consecutive integers on which a character is constant**Moscow Journal of Combinatorics and Number Theory 2012, vol.2, iss. 1, pp. 56-72.

**The least inert prime in a real quadratic field**, Mathematics of Computation, vol. 81, no. 279, July 2012, pp. 1777-1797.

**Multi-dimensional Frobenius problem**(with J. Amos, I. Pascu, V. Ponomarenko and Y. Zhang), Involve, a Journal of Mathematics 4-2 (2011), 187—197.

**On the counting function for the generalized Niven numbers**(with R. Daileda, J. Jou, R. Lemke-Oliver and E. Rossolimo), J. Théor. Nombres Bordeaux 21 (2009), no. 3, 503—515.

##### Preprints

**The Burgess inequality and the least k-th power non-residue** submitted.

**The smoothed Pólya-Vinogradov inequality** (with K. Adamczewski) submitted.

**The least k-th power non residue** accepted at the Journal of Number Theory.

#### Contact

**Phone:** 847-735-6187

**Email:** trevino@lakeforest.edu

**Personal Website:** http://campus.lakeforest.edu/trevino