Abstract:
Nutritional fads in the health and fitness world are constantly changing. Each new craze has its believers and critics. For the consumer, “what to believe” becomes a topic filled with uncertainty. This paper presents a systematic approach to understanding what consumers believe about the health messaging of “raw beverages”. The paper presents both substantive results from US consumers, as well as demonstrates a general approach by which researchers can more deeply understand the consumer mind with respect to the specifics of health and wellness issues.

Abstract:
We show how the Weil representation corresponding to the discriminant form of an even lattice $M$ can be viewed as the tensor product, over all primes, of finite-dimensional sub-representations of the Weil representations of $Mp_{2}(\mathbb{Q}_{p})$ on $M\otimes\mathbb{Q}_{p}$ restricted to $Mp_{2}(\mathbb{Z}_{p})$. Together with determining the elements in the metaplectic double cover $Mp_{2}(\mathbb{Q}_{p})$ in terms of the Weil indices of the quadratic form and related forms, we obtain a direct proof of the formula for the action of a general element of $Mp_{2}(\mathbb{Z})$ on $\mathbb{C}[M^{*}/M]$ described by Scheithauer and by Str\"omberg.

Abstract:
We show how to obtain the difference function of the Weierstrass Zeta function very directly, by choosing an appropriate order of summation for the series defining this function. As a byproduct, we show how to obtain the quasi-modularity of the weight 2 Eisenstein series immediately from the fact that it appears in this difference function and the homogeneity properties of the latter.

Abstract:
We generalize the elementary methods presented in several examples in the book \cite{[FZ]} to obtain the Thomae formulae for general fully ramified $Z_{n}$ curves.

Abstract:
We prove that Heegner cycles of codimension m+1 inside Kuga-Sato type varieties of dimension 2m+1 are coefficients of modular forms of weight 3/2+m in the appropriate quotient group. The main technical tool for generating the necessary relations is a Borcherds style theta lift with polynomials. We also show how this lift defines a new singular Shimura-type correspondence from weakly holomorphic modular forms of weight 1/2-m to meromorphic modular forms of weight 2m+2.

Abstract:
We determine the normalizer in $SL_{2}(\mathbb{R})$ of several families of congruence subgroups of $SL_{2}(\mathbb{Z})$. In addition, we show how these tools can be used to evaluate the groups of automorphisms and the discriminant kernels of a large family of isotropic lattices of signature (2,1).

Abstract:
We define weight raising and weight lowering operators for automorphic forms on Grassmannians, and construct a lift from weakly holomorphic modular forms of weight $1-\frac{b_{-}}{2}-m$ and the Weil representation associated to an even lattice of signature $(2,b_{-})$ with even $b_{-}$ to meromorphic automorphic forms of weight $m+b_{-}$ on the Shimura variety associated to $L$ having poles of order $m+b_{-}$ along rational quadratic divisors.

Abstract:
We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups arising from different weights are isomorphic since they are conjugate. We also prove a result about the intersection of two generalized Riordan with different weights.

Abstract:
We show how several results about p-adic lattices generalize easily to lattices over valuation ring of arbitrary rank having only the Henselian property for quadratic polynomial. If 2 is invertible we obtain the uniqueness of the Jordan decomposition and the Witt Cancelation Theorem. We show that the isomorphism classes of indecomposable rank 2 lattices over such a ring in which 2 is not invertible are characterized by two invariants, provided that the lattices contain a primitive norm divisible by 2 of maximal valuation.

Abstract:
We extend the relation between quasi-modular forms and modular forms to a wider class of functions. We then relate both forms to vector-valued modular forms with symmetric power representations, and prove a general structure theorem for these vector-valued forms.