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Preface Todd Cochran e an d Rober t Dressie r note d th e commo n interest s o f numbe r theorists an d harmoni c analyst s i n thei r department , an d propose d a n NSF - CBMS conferenc e whos e purpos e woul d b e t o furthe r th e cross-fertilizatio n be - tween thes e tw o areas . Th e conferenc e too k plac e durin g th e wee k Ma y 21-25 , 1990, o n th e campu s o f Kansa s Stat e University , i n Manhatta n ("Th e Littl e Apple"), Kansas . Th e conferenc e wa s funde d b y NS F Gran t DMS-8912917 . In addition , NS A Gran t MDS-904-90-14-401 8 provide d th e trave l expense s o f a number o f graduates students , enablin g the m t o atten d th e conference . In additio n t o th e lecture s reporte d upo n i n thi s volume , th e conferenc e fea - tured th e followin g nin e major addresses : Speaker J. Bec k (Rutgers U. ) P. X . Gallaghe r (Columbia U. ) H. Iwanie c (Rutgers U. ) T. W . Korne r (Cambridge U. ) J.-F. Mel a (U. Paris XIII ) I. Z . Ruzs a (MTA, Budapest ) B. Saffar i (U. Paris XI ) G. Tenenbau m (U. Nancy ) R. C . Vaugha n (Imperial College ) Title New Applications of the Roth-Haldsz Method in Irregularities of Distribution Duality for long second Moments of Short Interval Densities Estimates for coefficients of L-functions Universal Fourier Series Remarkable Subgroups of the Circle Nouveaux sets of Trigonometric Polynomials: Halfway between Random and Regular An Account of extremal Problems on Polynomials with restricted Coefficients Fourier Transforms of Divisor Distributions: A Survey of Applications The Upper Bound for G(k) in Waring's Problem