Influential results by Swinnerton-Dyer
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
asked 6 hours ago
Zidane
26125
add a comment |
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
asked 6 hours ago
Zidane
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
add a comment |
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
asked 6 hours ago
Zidane
26125
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
asked 6 hours ago
Zidane
26125
asked 6 hours ago
Zidane
26125
asked 6 hours ago
Zidane
26125
asked 6 hours ago
Zidane
26125
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
add a comment |
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
add a comment |
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
answered 4 hours ago
Carlo Beenakker
73.2k9165274
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
answered 4 hours ago
Carlo Beenakker
73.2k9165274
add a comment |
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
answered 4 hours ago
Carlo Beenakker
73.2k9165274
add a comment |
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
answered 4 hours ago
Carlo Beenakker
73.2k9165274
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
answered 4 hours ago
Carlo Beenakker
73.2k9165274
answered 4 hours ago
Carlo Beenakker
73.2k9165274
answered 4 hours ago
Carlo Beenakker
73.2k9165274
answered 4 hours ago
Carlo Beenakker
73.2k9165274
73.2k9165274
add a comment |
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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