Influential results by Swinnerton-Dyer












5














The conjecture of Birch and Swinnerton-Dyer had a tremendous influence on the development of arithmetic geometry. Which other results of Swinnerton-Dyer have had a lasting influence?






nt.number-theory ho.history-overview







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  • 2




    I am not a number theorist, but what is the evidence for the claim in your first sentence?
    – Yemon Choi
    6 hours ago






  • 5




    That you can't bid 8 diamonds as a sacrifice in bridge.
    – literature-searcher
    6 hours ago






  • 7




    Sir Peter Swinnerton-Dyer passed away on December 26th: en.wikipedia.org/wiki/Peter_Swinnerton-Dyer In the area of rational points, Swinnerton-Dyer had a huge influence, e.g., his papers on rational points on cubic hypersurfaces.
    – Jason Starr
    6 hours ago






  • 2




    His name appeared in several lines in Modern Chess Openings, 10th edition, mostly in offbeat variations such as the Ponziani. I don't know whether his lines have survived to the 15th edition. shropshirechess.org/History/1950s.htm
    – Gerry Myerson
    47 mins ago


















5














The conjecture of Birch and Swinnerton-Dyer had a tremendous influence on the development of arithmetic geometry. Which other results of Swinnerton-Dyer have had a lasting influence?






nt.number-theory ho.history-overview







share|cite|improve this question


















  • 2




    I am not a number theorist, but what is the evidence for the claim in your first sentence?
    – Yemon Choi
    6 hours ago






  • 5




    That you can't bid 8 diamonds as a sacrifice in bridge.
    – literature-searcher
    6 hours ago






  • 7




    Sir Peter Swinnerton-Dyer passed away on December 26th: en.wikipedia.org/wiki/Peter_Swinnerton-Dyer In the area of rational points, Swinnerton-Dyer had a huge influence, e.g., his papers on rational points on cubic hypersurfaces.
    – Jason Starr
    6 hours ago






  • 2




    His name appeared in several lines in Modern Chess Openings, 10th edition, mostly in offbeat variations such as the Ponziani. I don't know whether his lines have survived to the 15th edition. shropshirechess.org/History/1950s.htm
    – Gerry Myerson
    47 mins ago
















5












5








5







The conjecture of Birch and Swinnerton-Dyer had a tremendous influence on the development of arithmetic geometry. Which other results of Swinnerton-Dyer have had a lasting influence?






nt.number-theory ho.history-overview







share|cite|improve this question













The conjecture of Birch and Swinnerton-Dyer had a tremendous influence on the development of arithmetic geometry. Which other results of Swinnerton-Dyer have had a lasting influence?






nt.number-theory ho.history-overview




nt.number-theory ho.history-overview






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked 6 hours ago









Zidane

26125




26125








  • 2




    I am not a number theorist, but what is the evidence for the claim in your first sentence?
    – Yemon Choi
    6 hours ago






  • 5




    That you can't bid 8 diamonds as a sacrifice in bridge.
    – literature-searcher
    6 hours ago






  • 7




    Sir Peter Swinnerton-Dyer passed away on December 26th: en.wikipedia.org/wiki/Peter_Swinnerton-Dyer In the area of rational points, Swinnerton-Dyer had a huge influence, e.g., his papers on rational points on cubic hypersurfaces.
    – Jason Starr
    6 hours ago






  • 2




    His name appeared in several lines in Modern Chess Openings, 10th edition, mostly in offbeat variations such as the Ponziani. I don't know whether his lines have survived to the 15th edition. shropshirechess.org/History/1950s.htm
    – Gerry Myerson
    47 mins ago
















  • 2




    I am not a number theorist, but what is the evidence for the claim in your first sentence?
    – Yemon Choi
    6 hours ago






  • 5




    That you can't bid 8 diamonds as a sacrifice in bridge.
    – literature-searcher
    6 hours ago






  • 7




    Sir Peter Swinnerton-Dyer passed away on December 26th: en.wikipedia.org/wiki/Peter_Swinnerton-Dyer In the area of rational points, Swinnerton-Dyer had a huge influence, e.g., his papers on rational points on cubic hypersurfaces.
    – Jason Starr
    6 hours ago






  • 2




    His name appeared in several lines in Modern Chess Openings, 10th edition, mostly in offbeat variations such as the Ponziani. I don't know whether his lines have survived to the 15th edition. shropshirechess.org/History/1950s.htm
    – Gerry Myerson
    47 mins ago










2




2




I am not a number theorist, but what is the evidence for the claim in your first sentence?
– Yemon Choi
6 hours ago




I am not a number theorist, but what is the evidence for the claim in your first sentence?
– Yemon Choi
6 hours ago




5




5




That you can't bid 8 diamonds as a sacrifice in bridge.
– literature-searcher
6 hours ago




That you can't bid 8 diamonds as a sacrifice in bridge.
– literature-searcher
6 hours ago




7




7




Sir Peter Swinnerton-Dyer passed away on December 26th: en.wikipedia.org/wiki/Peter_Swinnerton-Dyer In the area of rational points, Swinnerton-Dyer had a huge influence, e.g., his papers on rational points on cubic hypersurfaces.
– Jason Starr
6 hours ago




Sir Peter Swinnerton-Dyer passed away on December 26th: en.wikipedia.org/wiki/Peter_Swinnerton-Dyer In the area of rational points, Swinnerton-Dyer had a huge influence, e.g., his papers on rational points on cubic hypersurfaces.
– Jason Starr
6 hours ago




2




2




His name appeared in several lines in Modern Chess Openings, 10th edition, mostly in offbeat variations such as the Ponziani. I don't know whether his lines have survived to the 15th edition. shropshirechess.org/History/1950s.htm
– Gerry Myerson
47 mins ago






His name appeared in several lines in Modern Chess Openings, 10th edition, mostly in offbeat variations such as the Ponziani. I don't know whether his lines have survived to the 15th edition. shropshirechess.org/History/1950s.htm
– Gerry Myerson
47 mins ago












1 Answer
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Just to show the limited value of citation counts, the most cited paper of Sir Peter Swinnerton-Dyer on MathSciNet is not his 1965 paper with Birch, but a 1954 paper with Atkin on Some properties of partitions:




In their paper, Atkin and Swinnerton-Dyer proved the startling fact
that for the three values $m = 5, 7, 11$ and every value of $r
= 0, 1, ... ,m -1$ the generating function $$sum_{ngeq 0}p(mn+r)q^n,$$ with $p(n)$ the number of partitions of $n$, is
congruent modulo $m$ to a simple infinite product.




as discussed in: Winquist and the Atkin-Swinnerton-Dyer partition congruences for modulus 11






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    2














    Just to show the limited value of citation counts, the most cited paper of Sir Peter Swinnerton-Dyer on MathSciNet is not his 1965 paper with Birch, but a 1954 paper with Atkin on Some properties of partitions:




    In their paper, Atkin and Swinnerton-Dyer proved the startling fact
    that for the three values $m = 5, 7, 11$ and every value of $r
    = 0, 1, ... ,m -1$     the generating function $$sum_{ngeq 0}p(mn+r)q^n,$$ with $p(n)$ the number of partitions of $n$, is
    congruent modulo $m$ to a simple infinite product.




    as discussed in: Winquist and the Atkin-Swinnerton-Dyer partition congruences for modulus 11






    share|cite|improve this answer


























      2














      Just to show the limited value of citation counts, the most cited paper of Sir Peter Swinnerton-Dyer on MathSciNet is not his 1965 paper with Birch, but a 1954 paper with Atkin on Some properties of partitions:




      In their paper, Atkin and Swinnerton-Dyer proved the startling fact
      that for the three values $m = 5, 7, 11$ and every value of $r
      = 0, 1, ... ,m -1$       the generating function $$sum_{ngeq 0}p(mn+r)q^n,$$ with $p(n)$ the number of partitions of $n$, is
      congruent modulo $m$ to a simple infinite product.




      as discussed in: Winquist and the Atkin-Swinnerton-Dyer partition congruences for modulus 11






      share|cite|improve this answer
























        2












        2








        2






        Just to show the limited value of citation counts, the most cited paper of Sir Peter Swinnerton-Dyer on MathSciNet is not his 1965 paper with Birch, but a 1954 paper with Atkin on Some properties of partitions:




        In their paper, Atkin and Swinnerton-Dyer proved the startling fact
        that for the three values $m = 5, 7, 11$ and every value of $r
        = 0, 1, ... ,m -1$         the generating function $$sum_{ngeq 0}p(mn+r)q^n,$$ with $p(n)$ the number of partitions of $n$, is
        congruent modulo $m$ to a simple infinite product.




        as discussed in: Winquist and the Atkin-Swinnerton-Dyer partition congruences for modulus 11






        share|cite|improve this answer












        Just to show the limited value of citation counts, the most cited paper of Sir Peter Swinnerton-Dyer on MathSciNet is not his 1965 paper with Birch, but a 1954 paper with Atkin on Some properties of partitions:




        In their paper, Atkin and Swinnerton-Dyer proved the startling fact
        that for the three values $m = 5, 7, 11$ and every value of $r
        = 0, 1, ... ,m -1$         the generating function $$sum_{ngeq 0}p(mn+r)q^n,$$ with $p(n)$ the number of partitions of $n$, is
        congruent modulo $m$ to a simple infinite product.




        as discussed in: Winquist and the Atkin-Swinnerton-Dyer partition congruences for modulus 11







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 4 hours ago









        Carlo Beenakker

        73.2k9165274




        73.2k9165274






























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