## Nicolas Robles

J L Doob Research Assistant Professor

### Contact Information

Office Address:

241, Illini Hall

Telephone: 217-265-5225

E-mail: nirobles ... this school

Mailing Address:

Department of Mathematics

University of Illinois at Urbana-Champaign

1409 W. Green Street (MC-382)

Urbana, IL 61801

### About me

Since July 2018, I have been a quant analyst at BofA in Chicago.

From August 2015 to August 2018, I was a Doob postdoc in the Mathematics Department of the University of Illinois at Urbana-Champaign. I also worked for Wolfram and for the CQF program.

In May 2015, I finished my doctoral thesis at the I-Math of UZH in Zurich, Switzerland. My supervisors were Alberto Cattaneo and Ashkan Nikeghbali and I was partially supported by the Forschungskredit grant K-71104-04-0.

Before joining the I-Math I took Part III of the Mathematical Tripos at the University of Cambridge (my thesis was on quantum rate-distortion theory).

Prior to that, I also completed the highly, highly recommended M.Sc. in Quantum Fields and Fundamental Forces at Imperial College London (this time my thesis was on zeta function regularization).

Previously, I worked in investment banking in London and Zurich (JPMorgan, Nomura and UBS).

### Research

My interests are primarily in number theory, theoretical physics and quantitative finance. I like to keep it as orthogonal as possible.

### Publications

__POST-DOCTORAL PAPERS__ (2015 - 2018)

**(17) Breaking the 1/2 barrier for the twisted second moment of Dirichlet L-functions**

joint work H. M. Bui, K. Pratt and A. Zaharescu

*Advances in Mathematics*(doi.org/10.1016/j.aim.2020.107175)

**(16) Unexpected average values of generalized von Mangoldt functions in residue classes**

joint work with A. Roy

*Journal of the Australian Mathematical Society*(10.1017/S1446788719000715)

**(15) Random permutations with logarithmic cycle weights**

joint work D. Zeindler

*Ann. Inst. Henri Poincaré Probab. Stat.*(1593137316)

**(14) More than five-twelfths of the zeros of ζ are on the critical line**

joint work with K. Pratt, A. Zaharescu and D. Zeindler

*Research in the Mathematical Sciences*(10.1007/s40687-019-0199-8)

**(13) On mean values of mollifiers and**

*L*-functions associated to primitive cusp formsjoint work with P. Kühn and D. Zeindler

*Mathematische Zeitschrift*(10.1007/s00209-018-2099-9)

**(12) Perturbed moments and a longer mollifier for critical zeros of ζ**

joint work with K. Pratt

*Research in Number Theory*(10.1007/s40993-018-0103-4)

**(11) Zeros of normalized combinations of ξ**

^{(k)}(*s*) on Re(*s*)=1/2joint work with S. Chaubey, A. Malik and A. Zaharescu

*Journal of Mathematical Analysis and Applications*(10.1016/j.jmaa.2017.12.045)

**(10) Polynomial partition asymptotics**

joint work with A. Dunn

*Journal of Mathematical Analysis and Applications*(10.1016/j.jmaa.2017.10.051)

**(9) The largest gap between zeros of entire**

*L*-functions is less than 41.54joint work with P. Kühn and A. Zaharescu

*Journal of Mathematical Analysis and Applications*(10.1016/j.jmaa.2016.12.007)

**(8) On a mollifier of the perturbed Riemann zeta-function**

joint work with P. Kühn and D. Zeindler

*Journal of Number Theory*(10.1016/j.jnt.2016.09.022)

**(7) Moments of averages of generalized Ramanujan sums**

joint work with A. Roy

*Monatshefte für Mathematik*(10.1007/s00605-016-0907-z)

__DOCTORAL PAPERS__(2011 - 2015)**(6) Koshliakov kernel and identities involving the Riemann zeta function**

joint work with A. Dixit, A. Roy and A. Zaharescu

*Journal of Mathematical Analysis and Applications*(10.1016/j.jmaa.2015.11.007)

**(5) Twisted second moments of the Riemann zeta-function and applications**

joint work with A. Roy and A. Zaharescu

*Journal of Mathematical Analysis and Applications*(10.1016/j.jmaa.2015.08.064)

**(4) Explicit formulas of a generalized Ramanujan sum**

joint work with P. Kühn

*International Journal of Number Theory*(10.1142/S1793042116500238)

**(3) Zeros of combinations of the Riemann ξ-function on bounded vertical shifts**

joint work with A. Dixit, A. Roy and A. Zaharescu

*Journal of Number Theory*(10.1016/j.jnt.2014.10.004)

**(2) Zeta functions on tori using contour integration**

joint work with E. Elizalde, K. Kirsten and F. L. Williams

*Int. J. Geom. Methods Mod. Phys.*(10.1142/S021988781550019X)

**(1) On a class of functions that satisfies explicit formulae involving the μ function**

joint work with P. Kühn and A. Roy

*The Ramanujan Journal*(10.1007/s11139-014-9608-1)

### Teaching

**(8) Differential Equations**

Summer 2018, MATH441 website link

**(7) Calculus II**

Spring 2018, MATH231 website link

**(6) Calculus III**

Fall 2017, MATH241 website link

**(5) Multivariable Calculus (Harvard University)**

Summer 2017, MATH21a (Oliver Knill) website link

**(4) Analytic Theory of Numbers II**

Spring 2017, MATH532 website link

**(3) Probability Theory**

Fall 2016, MATH461 website link

**(2) Introduction to Matrix Theory**

Spring 2016, MATH225 website link

**(1) Elementary Theory of Numbers**

Fall 2015, MATH453 website link