47 Double square moments and bounds for resonance sums for cusp forms 19:30 Geodesic restrictions of Maass forms and moments of Hecke L-functions 57:17 Twisted first moment of GL(3)×GL(2) 23:49 Quantum variance for automorphic forms 23:13 PATKÓS BALÁZS_ INDUCED AND NON-INDUCED POSET...
We consider the sawtooth function , with defined as the unique real number in that is equal to mod . We consider a (Borel) probability measure on the real line, and then compute the average value of this sawtooth function as well as various dilates of this expectation. Since is ...
With the advent of ad blockers, it seemed like we were just on the cusp of distraction-free web browsing—and then data privacy regulations had to come along. Now, nearly every website has to bombard you with cookie popups and banners before you can get to the content you actually wante...
there has also been agrowing consensusthat we could be on the cusp of replicating more general intelligence similar to that seen in humans — known as artificial general intelligence (AGI). "It really cannot be overemphasized how pivotal a shift this has been for the field," said Sara ...
Students can investigate whether the school they're attending, or considering attending, is on the cusp of closure. Information-seekers can look at the Department of Education's list of schools under scrutiny, called heightened cash monitoring. From this, prospective and current ...
13 July, 2008 in math.NT, paper | Tags: Mobius function, nilsequences, Ratner's theorem, Vaughan's identity, Vinogradov's method | by Terence Tao | 13 comments Ben Green and I have just uploaded to the arXiv our paper, “The Möbius function is asymptotically orthogonal to nilsequenc...
How many layers does a human tooth have? What is the difference between Gingivitis and Periodontitis? How successful are root canals treatment? What is the outermost white part of the teeth is called? What does early tooth decay look like? In which permanent teeth the steepest cusp incline is...
Is zero continuously differentiable? The absolute value function is continuous (i.e. it has no gaps). Itis differentiable everywhere except atthe point x = 0, where it makes a sharp turn as it crosses the y-axis. A cusp on the graph of a continuous function. At zero, the function is...
I just went to a talk and there was one tiny example the speaker gave to explain when something is not a manifold. I liked it so much I thought I'd dedicate an entire blog post to what was half a line on a board. I defined manifolds a long time ago, but
Artificial intelligence has come a long way in recent years. Fromcomputational photographyto self-driving cars, we’ve seen the technology unlock new possibilities and disrupt entire industries. Now, we’re seemingly at the cusp of another revolution with ChatGPT, which can generate text with nearl...