Analytic Number Theory: Proceedings of a Conference In Honor by Krishnaswami Alladi (auth.), Bruce C. Berndt, Harold G.

By Krishnaswami Alladi (auth.), Bruce C. Berndt, Harold G. Diamond, Adolf J. Hildebrand (eds.)

On might sixteen -20, 1995, nearly one hundred fifty mathematicians collected on the convention heart of the college of Illinois at Allerton Park for an Inter­ nationwide convention on Analytic quantity conception. The assembly marked the upcoming reputable retirement of Heini Halberstam from the maths fac­ ulty of the college of Illinois at Urbana-Champaign. Professor Halberstam has been on the college considering the fact that 1980, for eight years as head of the dept of arithmetic, and has been a number one researcher and instructor in quantity conception for over 40 years. this system integrated invited one hour lectures via G. Andrews, J. Bour­ achieve, J. M. Deshouillers, H. Halberstam, D. R. Heath-Brown, H. Iwaniec, H. L. Montgomery, R. Murty, C. Pomerance, and R. C. Vaughan, and virtually 100 different talks of various lengths. those volumes include contributions from lots of the central audio system and from some of the different members, in addition to a few papers from mathematicians who have been not able to wait. The contents span a wide diversity of topics from modern quantity concept, with the bulk having an analytic flavor.

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Math. , Providence 1988. George E. edu On subset-sum-distinct sequences Jaegug Bae Dedicated to Professor Halberstam on the occasion of his retirement Abstract. We use TomiC's inequality to show some interesting properties of subset-sum-distinct sequences including an elementary proof of a theorem of Steele, Hanson, and Stenger. Also, we comment on a theorem of L. Moser. 1. Introduction In this paper, by a sequence we mean a strictly increasing sequence of positive integers. We start with a definition.

We must also note the work of Rousselet [26] (both upper and lower bounds) in the interval The method we present here will improve all these results up to XO. 56 • Before stating our main result, we fix an arbitrarily small positive absolute constant f. lResearch supported in part by a grant from the National Science Foundation 40 R. C. BAKER AND G. HARMAN Theorem 1. 241. 48 and C 1 = < 0 < - + 10- 10 °. 1 - f 2 Our theorem may also be compared to the following result of Bombieri, Friedlander and Iwaniec [5].

M,n q imn=a(mod q) We shall discuss Type II2,1/a,IIII sums here. We will require estimates for type 12 ,13 sums in sections 7 and 8 respectively. In this section we appeal to the work of Bombieri, Friedlander and Iwaniec [3,4]j only the first of these was available to Fouvry when he wrote [11], and this is one factor which leads to our improved result. The further paper [5] is not of much direct help to us. All these depend in an essential way on the work of Deshouillers and Iwaniec [7] on Kloosterman sums, and so prevent our results from being uniform in a.

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