We determine local test vectors for Waldspurger functionals for GL 2 , in the case where both the representation of GL 2 and the character of the degree two extension are ramified, with certain restrictions. We use this to obtain an explicit version of Waldspurger's formula relating twisted central L-values of automorphic representations on GL 2 with certain toric period integrals. As a consequence, we generalize an average value formula of Feigon and Whitehouse, and obtain some nonvanishing results. 1

Introduction and hypothesis The aim of this study was to measure physiologic and psychologic stress reactivity in women with overactive bladder (OAB). There is growing evidence in preclinical models that central nervous system dysregulation, particularly in response to psychological stress, may contribute to lower urinary tract symptoms in women with OAB. Methods Postmenopausal women with OAB and healthy controls underwent Structured Clinical Interview for DSM-IV Axis I disorders (SCID) to identify those without identifiable psychiatric disease. Eligible participants underwent physiologic measures including basal (cortisol-awakening response; CAR) and stress-activated salivary cortisol levels, heart rate (HR), urinary metanephrines and neurotrophins, as well as validated symptom assessment for stress, anxiety, depression, and bladder dysfunction at baseline and during, and following an acute laboratory stressor, the Trier Social Stress Test (TSST). Results Baseline measures of cortisol reactivity measured by CAR showed blunted response among women with OAB (p = 0.015), while cortisol response to the TSST was greater in the OAB group (p = 0.019). Among OAB patients, bladder urgency as measured by visual analog scale (VAS) increased from pre- to post-TSST (p = 0.04). There was a main effect of TSST on HR (p < 0.001), but no group interaction. Conclusions Preliminary findings suggest that women with OAB have greater physiologic and psychologic stress reactivity than healthy controls. Importantly for women with OAB, acute stress appears to exacerbate bladder urgency. Evaluation of the markers of stress response may suggest targets for potential diagnostic and therapeutic interventions.

We revisit a classical result of Howe and Pitatski-Shapiro on the failure of strong multiplicity one for GSp(4).

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I give a new integral representation for the degree five (standard) L-function for automorphic representations of GSp(4) that is a refinement of integral representation of Piatetski-Shapiro and Rallis. The new integral representation unfolds to produce the Bessel model for GSp (4) which is a unique model. The local unramified calculation uses an explicit formula for the Bessel model and differs completely from Piatetski-Shapiro and Rallis.