Category Archives: Number theory

Dan Romik on the Riemann zeta function

This post, about the Riemann zeta function, which is among the most important and mysterious mathematical objects was kindly written by Dan Romik. It is related to his paper Orthogonal polynomial expansions for the Riemann xi function,  that we mentioned … Continue reading

Posted in Combinatorics, Guest blogger, Number theory | Tagged , , , , | 1 Comment

8866128975287528³+(-8778405442862239)³+(-2736111468807040)³

Update: The result was achieved by Andrew Booker from Bristol. Here is the preprint Cracking the problem with 33. It is a notoriously difficult open problem which integers can be written as the sum of three integer cubes.  Such integers … Continue reading

Posted in Number theory | Tagged | 17 Comments

Test Your Intuition (or knowledge, or programming skills) 36

How much is   The product ranges over all primes. In other words, Just heard it from Avinoam Mann.  

Posted in Number theory, Test your intuition | Tagged | 12 Comments

Dan Romik Studies the Riemann’s Zeta Function, and Other Zeta News.

Updates to previous posts: Karim Adiprasito expanded in a comment to his post on the g-conjecture on how to move from vertex-decomposable spheres to general spheres. Some photos were added to the post: Three pictures. Dan Romik on the Zeta … Continue reading

Posted in Number theory, Updates | Tagged , , , , , , , , | 4 Comments

Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska: Universal optimality of the E8 and Leech lattices and interpolation formulas

Henry Cohn A follow up paper on the tight bounds for sphere packings in eight and 24 dimensions. (Thanks, again, Steve, for letting me know.) For the 2016 breakthroughs see this post, this post of John Baez, this article by Erica Klarreich on … Continue reading

Posted in Algebra, Combinatorics, Geometry, Number theory | Tagged , , , , , , , | 1 Comment

Jean

Jean Bourgain and Joram Lindenstrauss. I was very sad to hear that Jean Bourgain, among the greatest mathematicians of our time, and a dear friend, passed away.  I first met Jean about forty years ago and later we  became friends … Continue reading

Posted in Analysis, Combinatorics, Computer Science and Optimization, Convexity, Number theory, Obituary | Tagged | 4 Comments

Akshay Venkatesh Lectures at HUJI – Ostrowski’s Prize Celebration, January 24&25

Thursday January 25, 14:15-15:45 Ostrowski’s prize ceremony and Akshay Venkatesh’s prize lecture: Period maps and Diophantine problems Followed by a Basic notion lecture by Frank Calegary 16:30-17:45: The cohomology of arithmetic groups and Langlands program Wednesday January 24, 18:00-17:00: Akshay Venkatesh … Continue reading

Posted in Computer Science and Optimization, Geometry, Number theory, Updates | Tagged , , | Leave a comment

Updates (belated) Between New Haven, Jerusalem, and Tel-Aviv

This is a (very much) belated update post from the beginning of March (2016). New Haven I spent six weeks in February (2016) in New Haven. It was very nice to get back to Yale after more than two years. Here … Continue reading

Posted in Art, Combinatorics, Computer Science and Optimization, Number theory, Updates | Leave a comment

EDP Reflections and Celebrations

The Problem In 1932, Erdős conjectured: Erdős Discrepancy Conjecture (EDC)  [Problem 9 here] For any constant , there is an such that the following holds. For any function , there exists an   and a   such that For any , … Continue reading

Posted in Combinatorics, Number theory | Tagged , | 4 Comments

Polymath 8 – a Success!

Yitang Zhang Update (July 22, ’14). The polymath8b paper “Variants of the Selberg sieve, and bounded intervals containing many primes“, is now on the arXiv. See also this post on Terry Tao’s blog. Since the last update, we also had here … Continue reading

Posted in Mathematics over the Internet, Number theory, Open problems | Tagged , , , , | 10 Comments