Nickolas Andersen
= Nickolas Andersen
{c}
<Nickolas Andersen> studies <analytic number theory>, <modular forms> and <L-functions>. With <Jeffrey C. Lagarias> and <Robert C. Rhoades>, he studied <shifted polyharmonic Maass forms>, which replace an <eigenfunction> equation by
$$
(\Delta_k-\lambda)^m f=0.
$$
Here $\Delta_k$ is a weight-dependent <hyperbolic Laplacian>; the functions also obey arithmetic symmetry and controlled growth. The study proves finite dimensionality and describes the role of <Eisenstein series> and their parameter derivatives. https://math.byu.edu/directory/andersen-nickolas[Institutional profile, Research Interests]{ref}<Shifted polyharmonic Maass forms for PSL(2,Z) by Nickolas Andersen and others>[Introduction, equations (1.1)–(1.3) and Theorem 1.1]{ref}
The mechanism is visible by differentiating a family of <eigenfunctions>. If $L E(s)=\lambda(s)E(s)$ and $L$ is independent of $s$, then
$$
(L-\lambda(s))\frac{\partial E}{\partial s}=\lambda'(s)E(s).
$$
At a fixed parameter value, applying $L-\lambda$ again gives zero. A derivative can therefore yield a generalized solution of depth two instead of another ordinary <eigenfunction>. The arithmetic symmetry and growth requirements still need checking; the operator identity explains the construction's motivation.
\Image[https://brigham-young-brightspot-us-east-2.s3.us-east-2.amazonaws.com/79/0d/33944c874a1aab6ab12ba50dcf5b/andersen-nick-06.jpg]
{title=Nickolas Andersen}
{description=Portrait identified on https://math.byu.edu/directory/andersen-nickolas[the Brigham Young University Mathematics profile].}
{height=300}