Boris Mezhericher's Homepage
Welcome. I am a quantitative researcher, interested in data mining, predictive analytics, and market microstructure. Before graduating in
2008, I was working in computational number theory with my advisor, Dorian Goldfeld. My Ph.D. thesis was a combination of the results below, on computational aspects of
Maass forms for SL(3,Z).
Research
 Evaluating Jacquet's Whittaker
functions and Maass forms for SL(3,Z)
We present and compare
several
algorithms for evaluating the Whittaker functions for SL(3,Z).
We apply one of the algorithms to the problem of evaluating a Maass
form for SL(3,Z) with known eigenvalues and Fourier coefficients. A
computer program which implements all these algorithms can be downloaded
below and can be used for empirical experimentation with
recently discovered Maass forms. (For example, see an informal automorphy check of Ce Bian's first example of a
generic Maass form for SL(3,Z).)
 Hypergeometric functions, Lfunction identities and computation
We present identities arizing from the functional equations of higher
degree Lfunctions. These identities can be viewed as a generalization of
the Voronoi summation formula of Miller & Schmid and Goldfeld & Li.
Using these identities, we propose an algorithm for computing the
Dirichlet coefficients of higher degree Lfunctions.
Code
 Algorithms to compute Whittaker functions and to evaluate Maass forms
given eigenvalues and Fourier coefficients are implemented in
PARI/GP and can be
downloaded here or (better) from GitHub. Instructions are here.
Contact Info
