Mixing
A conjecture of Littlewood
Clash Royale CLAN TAG#URR8PPP
up vote
1
down vote
favorite
The following is a conjecture due to Littlewood
For any set of non-zero integers $n_1,cdots,n_k$ the inequality
$$int_0^2pi|1+e^in_1x+cdots+e^in_kx|dxgeq Clog k$$
holds.
Is this proven to be true(or false)?
cv.complex-variables inequalities
asked 3 hours ago
BigM
7221925
add a comment |Â
up vote
1
down vote
favorite
The following is a conjecture due to Littlewood
For any set of non-zero integers $n_1,cdots,n_k$ the inequality
$$int_0^2pi|1+e^in_1x+cdots+e^in_kx|dxgeq Clog k$$
holds.
Is this proven to be true(or false)?
cv.complex-variables inequalities
asked 3 hours ago
BigM
7221925
Yes, it's been proven. Too lazy to find reference now, but I'm pretty sure you can just google it.
– mathworker21
2 hours ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The following is a conjecture due to Littlewood
For any set of non-zero integers $n_1,cdots,n_k$ the inequality
$$int_0^2pi|1+e^in_1x+cdots+e^in_kx|dxgeq Clog k$$
holds.
Is this proven to be true(or false)?
cv.complex-variables inequalities
asked 3 hours ago
BigM
7221925
The following is a conjecture due to Littlewood
For any set of non-zero integers $n_1,cdots,n_k$ the inequality
$$int_0^2pi|1+e^in_1x+cdots+e^in_kx|dxgeq Clog k$$
holds.
Is this proven to be true(or false)?
cv.complex-variables inequalities
cv.complex-variables inequalities
asked 3 hours ago
BigM
7221925
asked 3 hours ago
BigM
7221925
asked 3 hours ago
BigM
7221925
asked 3 hours ago
BigM
7221925
asked 3 hours ago
BigM
7221925
7221925
Yes, it's been proven. Too lazy to find reference now, but I'm pretty sure you can just google it.
– mathworker21
2 hours ago
add a comment |Â
Yes, it's been proven. Too lazy to find reference now, but I'm pretty sure you can just google it.
– mathworker21
2 hours ago
Yes, it's been proven. Too lazy to find reference now, but I'm pretty sure you can just google it.
– mathworker21
2 hours ago
Yes, it's been proven. Too lazy to find reference now, but I'm pretty sure you can just google it.
– mathworker21
2 hours ago
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
5
down vote
accepted
This was proved by S. Konyagin [7] and independently by McGehee, Pigno, and Smith [13] in 1981. A short proof is available in [5].
[7] S.V. Konjagin, On a problem of Littlewood, Mathematics of the USSR, Izvestia, 18 (1981), 205–225. http://mi.mathnet.ru/eng/izv1556
[5] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
[13] O.C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L1 norm of exponential sums, Ann. Math. 113 (1981), 613–618. https://www.jstor.org/stable/2007000
answered 2 hours ago
literature-searcher
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
This was proved by S. Konyagin [7] and independently by McGehee, Pigno, and Smith [13] in 1981. A short proof is available in [5].
[7] S.V. Konjagin, On a problem of Littlewood, Mathematics of the USSR, Izvestia, 18 (1981), 205–225. http://mi.mathnet.ru/eng/izv1556
[5] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
[13] O.C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L1 norm of exponential sums, Ann. Math. 113 (1981), 613–618. https://www.jstor.org/stable/2007000
answered 2 hours ago
literature-searcher
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
5
down vote
accepted
This was proved by S. Konyagin [7] and independently by McGehee, Pigno, and Smith [13] in 1981. A short proof is available in [5].
[7] S.V. Konjagin, On a problem of Littlewood, Mathematics of the USSR, Izvestia, 18 (1981), 205–225. http://mi.mathnet.ru/eng/izv1556
[5] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
[13] O.C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L1 norm of exponential sums, Ann. Math. 113 (1981), 613–618. https://www.jstor.org/stable/2007000
answered 2 hours ago
literature-searcher
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
5
down vote
accepted
up vote
5
down vote
accepted
This was proved by S. Konyagin [7] and independently by McGehee, Pigno, and Smith [13] in 1981. A short proof is available in [5].
[7] S.V. Konjagin, On a problem of Littlewood, Mathematics of the USSR, Izvestia, 18 (1981), 205–225. http://mi.mathnet.ru/eng/izv1556
[5] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
[13] O.C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L1 norm of exponential sums, Ann. Math. 113 (1981), 613–618. https://www.jstor.org/stable/2007000
answered 2 hours ago
literature-searcher
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
This was proved by S. Konyagin [7] and independently by McGehee, Pigno, and Smith [13] in 1981. A short proof is available in [5].
[7] S.V. Konjagin, On a problem of Littlewood, Mathematics of the USSR, Izvestia, 18 (1981), 205–225. http://mi.mathnet.ru/eng/izv1556
[5] R.A. DeVore and G.G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
[13] O.C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L1 norm of exponential sums, Ann. Math. 113 (1981), 613–618. https://www.jstor.org/stable/2007000
answered 2 hours ago
literature-searcher
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
literature-searcher
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
literature-searcher
661
answered 2 hours ago
literature-searcher
661
661
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
literature-searcher is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f312265%2fa-conjecture-of-littlewood%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Yes, it's been proven. Too lazy to find reference now, but I'm pretty sure you can just google it.
– mathworker21
2 hours ago