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, L-function identities and computation
    We present identities arizing from the functional equations of higher degree L-functions. 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 L-functions.

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

  • Email: mboris@gmail.com