A shifted asymmetry index series

Shifted quadratic Zeta series

It is well known that the Riemann Zeta function ζ ( p ) = ∑∞n=1 1/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑∞ n=1 1/ ( 4n2−α2)p . In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form repre...

Special values of shifted convolution Dirichlet series

In a recent important paper, Hoffstein and Hulse [14] generalized the notion of Rankin-Selberg convolution L-functions by defining shifted convolution L-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.

Shifted Convolution Sums Involving Theta Series

Let f be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus and denote by λf (n) its n-th Hecke eigenvalue. Let r(n) = # { (n1, n2) ∈ Z : n21 + n22 = n } . In this paper, we study the shifted convolution sum Sh(X) = ∑ n≤X λf (n+ h)r(n), 1 ≤ h ≤ X, and establish uniform bounds with respect to the shift h for Sh(X).

Stokesian peristaltic pumping in a three-dimensional tube with a phase-shifted asymmetry

Many physiological flows are driven by waves of muscular contractions passed along a tubular structure. This peristaltic pumping plays a role in ovum transport in the oviduct and in rapid sperm transport through the uterus. As such, flow due to peristalsis has been a central theme in classical biological fluid dynamics. Analytical approaches and numerical methods have been used to study flow in...

Adaptive control of nonminimum-phase systems using shifted Laurent series