On the adjoint L-function of the p-adic GSp(4)

We explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of Gross-Prasad and Rallis in this case. The conjecture states that the adjoint L-function has a pole at s=1 if and only if the L-packet contains a generic representation.Comment: small corrections and improvements; to appear in J. Number Theor

THE IMPACT OF BIOFUEL POLICIES ON OVERSHOOTING OF AGRICULTURAL PRICES

The Federal Reserve has increased nominal interest rates since early 2016. It is expected that commodity prices will drop in response to this monetary intervention. The overshooting hypothesis explains that commodity prices are more flexible than manufacturing prices and therefore are more volatile. In this situation, it is expected that agricultural commodities decline significantly (i.e., overshoot) and gradually return to their long-run equilibrium. This adjustment behavior has implications for income stability and financial viability of farmers. This research contributes to the overshooting literature by including the energy sector in the overshooting model. The interlinks between energy and other sectors in the economy as well as the vast resource allocation to biofuel production in recent decades demand more attention to the impact of energy on the dynamic adjustment path of relative prices’ reaction to monetary shocks. We assume energy prices have independent adjustment path and include the links between the energy and agricultural sectors through biofuel production in our model. Our theoretical model shows that by including energy prices in the model, agricultural prices and the exchange rate overshoot less than the prediction of prior studies. This happens because we expect that flexible energy prices share the burden of the shock with other flexible prices in the model. We also describe how an increasing share of biofuels in the total fuel consumption will reduce the flexibility of energy prices. In our empirical analysis, we use monthly data from January 1975 to December 2017 for three producer price indexes (i.e., agricultural commodities, energy, and industrial goods), exchange rates, and money supply to test the overshooting hypothesis. We found the series to be nonstationary and cointegrated of the order one, I(1). Thus, we estimated a vector error correction model to identify the short run adjustment parameters while maintaining the long-run relationships between the variables. We identify and control for three possible structural breaks in the data that coincide with two economic crises and the biofuel production era. We also estimated the empirical model using a sub-sample from January 1975 to March 1999 and compared the results with the findings in previous studies. Our empirical results confirm the theoretical expectation that agricultural commodities adjust faster than manufacturing prices. The analysis of the impulse response functions shows that after a money supply shock, agricultural prices were the most responsive, followed by energy prices and exchange rates. In both full sample and the sub-sample, the volatility of prices and exchange rates happen during the first 5 to 10 months. The sluggish adjustment of manufacturing prices was evident from the corresponding impulse response functions. The empirical evidence rejects the long-run money neutrality, consistent with the findings of previous empirical studies. Compared to previous models, our empirical model shows that including energy prices will reduce the extent to which agricultural commodities overshoot. Therefore we expect the disturbances to the farm income variability, in response to monetary policy, to be less than what prior model would have estimated. In this regard, energy prices are a stabilizing factor in this model. We find that increased share of biofuel from total fuel consumption would positively affect the overshooting of agricultural prices. So, higher biofuel mandates could reduce the flexibility of the energy prices and therefore have an adverse effect on the farm price stability

On Combinatorics of the Arthur Trace Formula, Convex Polytopes, and Toric Varieties

We explicate the combinatorial/geometric ingredients of Arthur's proof of the convergence and polynomiality, in a truncation parameter, of his non-invariant trace formula. Starting with a fan in a real, finite dimensional, vector space and a collection of functions, one for each cone in the fan, we introduce a combinatorial truncated function with respect to a polytope normal to the fan and prove the analogues of Arthur's results on the convergence and polynomiality of the integral of this truncated function over the vector space. The convergence statements clarify the important role of certain combinatorial subsets that appear in Arthur's work and provide a crucial partition that amounts to a so-called nearest face partition. The polynomiality statements can be thought of as far extensions of the Ehrhart polynomial. Our proof of polynomiality relies on the Lawrence-Varchenko conical decomposition and readily implies an extension of the well-known combinatorial lemma of Langlands. The Khovanskii-Pukhlikov virtual polytopes are an important ingredient here. Finally, we give some geometric interpretations of our combinatorial truncation on toric varieties as a measure and a Lefschetz number