Around 1980, K. Doi and H. Hida found a meaning of the special value of certain degree 3 L-functions, so called adjoint L-functions of cusp forms. They discovered that if a prime divides “algebraic part” of the adjoint L-function of a cusp form, the prime is a congruence prime for the cusp form. E. Ghate and M. Dimitrov proved analogues of Hida’s theorem in Hilbert modular case. E. Urban also p...

Arithmetic Asian or average price options deliver payoffs based on the average underlying price over a prespecified time period. Asian options are an important family of derivative contracts with a wide variety of applications in currency, equity, interest rate, commodity, energy, and insurance markets. We derive two analytical formulas for the value of the continuously sampled arithmetic Asian...

In the theories of electrodynamics, acoustics, and optics, fields that satisfy the homogeneous wave equation are often represented by integral expansions of monochromatic plane waves, all propagating with the same speed [ 1,2] . Two different plane-wave expansions are in use. One expansion, due to Whittaker [3] , expresses the field as a superposition of monochromatic, homogeneous plane waves; ...

Let G be a (split connected) reductive group over Fq, and N be its maximal unipotent subgroup. Let BunN be the algebraic stack classifying N–bundles on a smooth projective curve X over Fq. V. Drinfeld has introduced a remarkable partial compactification BunN of BunN . In this paper we study the stack BunN and a certain category of perverse sheaves on it. Let us briefly explain our motivations (...

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Sanjay Basu and Russell Phillips discuss the findings from Whittaker and colleagues on the link between extending primary care hours and emergency department utilization.

We give explicit formulas for class one Whittaker functions on SOo(2, q) by examing the system of partial differential equations for their radial parts.