Brüdern, Jörg

[["dc.bibliographiccitation.firstpage","264"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","Mathematika"],["dc.bibliographiccitation.lastpage","277"],["dc.bibliographiccitation.volume","42"],["dc.contributor.author","Baker, R. C."],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:24Z"],["dc.date.available","2017-09-07T11:51:24Z"],["dc.date.issued","1995"],["dc.identifier.doi","10.1112/S0025579300014583"],["dc.identifier.gro","3146112"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3859"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0025-5793"],["dc.title","Cubic Diophantine inequalities"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","419"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Glasgow Mathematical Journal"],["dc.bibliographiccitation.lastpage","434"],["dc.bibliographiccitation.volume","44"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Kawada, K."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:20Z"],["dc.date.available","2017-09-07T11:51:20Z"],["dc.date.issued","2002"],["dc.description.abstract","We discuss the representation of primes, almost-primes, and related arithmetic sequences as sums of kth powers of natural numbers. In particular, we show that on GRH, there are infinitely many primes represented as the sum of 2\\lceil 4k/3\\rceil positive integral kth powers, and we prove unconditionally that infinitely many P_2-numbers are the sum of 2k+1 positive integral kth powers. The sieve methods required to establish the latter conclusion demand that we investigate the distribution of sums of kth powers in arithmetic progressions, and our conclusions here may be of independent interest."],["dc.identifier.doi","10.1017/S0017089502030070"],["dc.identifier.gro","3146079"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3822"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0017-0895"],["dc.title","Additive representation in thin sequences, VI: representing primes, and related problems"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","423"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","The Quarterly Journal of Mathematics"],["dc.bibliographiccitation.lastpage","436"],["dc.bibliographiccitation.volume","52"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Kawada, K."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:21Z"],["dc.date.available","2017-09-07T11:51:21Z"],["dc.date.issued","2001"],["dc.description.abstract","We describe a method for establishing that values from a fixed polynomial sequence are represented frequently by some prescribed sum of powers of natural numbers. As an illustration of this method, we show that for at least X129/136 of the integers n with 1 ≤ n ≤ X, a fixed quadratic polynomial φ(n) may be written as the sum of five cubes of positive integers. A similar result is established for the sum of a square and three cubes of positive integers."],["dc.identifier.doi","10.1093/qjmath/52.4.423"],["dc.identifier.gro","3146084"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3828"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0033-5606"],["dc.title","Additive Representation in Thin Sequences, IV: Lower Bound Methods"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","117"],["dc.bibliographiccitation.issue","1-2"],["dc.bibliographiccitation.journal","Mathematika"],["dc.bibliographiccitation.lastpage","125"],["dc.bibliographiccitation.volume","47"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Kawada, K."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:20Z"],["dc.date.available","2017-09-07T11:51:20Z"],["dc.date.issued","2000"],["dc.identifier.doi","10.1112/S002557930001576X"],["dc.identifier.gro","3146092"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3837"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0025-5793"],["dc.title","Additive representation in thin sequences, II: The binary Goldbach problem"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","739"],["dc.bibliographiccitation.issue","1738"],["dc.bibliographiccitation.journal","Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences"],["dc.bibliographiccitation.lastpage","761"],["dc.bibliographiccitation.volume","356"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Granville, A."],["dc.contributor.author","Perelli, A."],["dc.contributor.author","Vaughan, R. C."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:25Z"],["dc.date.available","2017-09-07T11:51:25Z"],["dc.date.issued","1998"],["dc.description.abstract","This paper is concerned with mean values of exponential sum generating functions over k–free numbers, and especially their L1–means. We also provide non–trivial estimates for the L1–means of such generating functions restricted to the minor arcs occurring in Hardy–Littlewood dissections, thereby permitting the circle method to be successfully applied to certain additive problems hitherto beyond its reach."],["dc.identifier.doi","10.1098/rsta.1998.0183"],["dc.identifier.gro","3146105"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3851"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","1364-503X"],["dc.title","On the exponential sum over k–free numbers"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","267"],["dc.bibliographiccitation.issue","3"],["dc.bibliographiccitation.journal","Acta Arithmetica"],["dc.bibliographiccitation.lastpage","289"],["dc.bibliographiccitation.volume","100"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Kawada, K."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:22Z"],["dc.date.available","2017-09-07T11:51:22Z"],["dc.date.issued","2001"],["dc.identifier.doi","10.4064/aa100-3-3"],["dc.identifier.gro","3146085"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3829"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0065-1036"],["dc.title","Additive representation in thin sequences, III: asymptotic formulae"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","41"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","The Quarterly Journal of Mathematics"],["dc.bibliographiccitation.lastpage","48"],["dc.bibliographiccitation.volume","54"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:20Z"],["dc.date.available","2017-09-07T11:51:20Z"],["dc.date.issued","2003"],["dc.identifier.doi","10.1093/qjmath/54.1.41"],["dc.identifier.gro","3146078"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3821"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0033-5606"],["dc.title","The paucity problem for certain pairs of diagonal equations"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","57"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Mathematika"],["dc.bibliographiccitation.lastpage","75"],["dc.bibliographiccitation.volume","46"],["dc.contributor.author","Balog, A."],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:24Z"],["dc.date.available","2017-09-07T11:51:24Z"],["dc.date.issued","1999"],["dc.description.abstract","Investigations concerning the gaps between consecutive prime numbers have long occupied an important position on the interface between additive and multiplicative number theory. Perhaps the most famous problem concerning these gaps, the Twin Prime Conjecture, asserts that the aforementioned gaps are infinitely often as small as 2. Although a proof of this conjecture seems presently far beyond our reach (but see [5] and [10] for related results), weak evidence in its favour comes from studying unusually short gaps between prime numbers. Thus, while it follows from the Prime Number Theorem that the average gap between consecutive primes of size about x is around log x, it is now known that such gaps can be infinitely often smaller than 0–249 log x (this is a celebrated result of Maier [12], building on earlier work of a number of authors; see in particular [7], [13], [3] and [11]). A conjecture weaker than the Twin Prime Conjecture asserts that there are infinitely many gaps between prime numbers which are powers of 2, but unfortunately this conjecture also seems well beyond our grasp. Extending this line of thought, Kent D. Boklan has posed the problem of establishing that the gaps between prime numbers infinitely often have only small prime divisors, and here the latter divisors should be small relative to the size of the small gaps established by Maier [12]. In this paper we show that the gaps between consecutive prime numbers infinitely often have only small prime divisors, thereby solving Boklan's problem. It transpires that the methods which we develop to treat Boklan's problem are capable also of detecting multiplicative properties of more general type in the differences between consecutive primes, and this theme we also explore herein."],["dc.identifier.doi","10.1112/S0025579300007567"],["dc.identifier.gro","3146099"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3844"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0025-5793"],["dc.title","On smooth gaps between consecutive prime numbers"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1197"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Compositio Mathematica"],["dc.bibliographiccitation.lastpage","1220"],["dc.bibliographiccitation.volume","140"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:19Z"],["dc.date.available","2017-09-07T11:51:19Z"],["dc.date.issued","2004"],["dc.identifier.doi","10.1112/S0010437X04001058"],["dc.identifier.gro","3146075"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3818"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0010-437X"],["dc.title","Additive representation in short intervals, I: Waring’s problem for cubes"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","173"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Michigan Mathematical Journal"],["dc.bibliographiccitation.lastpage","190"],["dc.bibliographiccitation.volume","47"],["dc.contributor.author","Brüdern, J."],["dc.contributor.author","Perelli, A."],["dc.contributor.author","Wooley, T. D."],["dc.date.accessioned","2017-09-07T11:51:24Z"],["dc.date.available","2017-09-07T11:51:24Z"],["dc.date.issued","2000"],["dc.identifier.doi","10.1307/mmj/1030374676"],["dc.identifier.gro","3146097"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/3842"],["dc.language.iso","en"],["dc.notes.status","final"],["dc.notes.submitter","chake"],["dc.relation.issn","0026-2285"],["dc.title","Twins of k-Free Numbers and Their Exponential Sum"],["dc.type","journal_article"],["dc.type.internalPublication","no"],["dc.type.peerReviewed","no"],["dspace.entity.type","Publication"]]