bio | website | stanford.edu/~rjlo |
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location | Palo Alto, CA | |
age | ||
visits | member for | 4 years, 4 months |
seen | 9 hours ago | |
stats | profile views | 312 |
Nov 30 |
asked | Is this extension of the Selberg class trivial? |
Nov 24 |
awarded | Yearling |
Aug 27 |
awarded | Yearling |
Aug 27 |
awarded | Yearling |
Aug 25 |
revised |
The behavior of a certain greedy algorithm for Erdős Discrepancy Problem
added 971 characters in body |
Aug 25 |
revised |
The behavior of a certain greedy algorithm for Erdős Discrepancy Problem
added 550 characters in body |
Aug 25 |
comment |
The behavior of a certain greedy algorithm for Erdős Discrepancy Problem
I will add data for the squarefree problem to my answer in a second, but let me just quickly give you the gist -- it's the same basic behavior, with $1/3$ appearing just as clearly. |
Aug 25 |
comment |
The behavior of a certain greedy algorithm for Erdős Discrepancy Problem
His. And the ratio of $\log D/\log N$ I alluded to, not in graph form: 0.3010299957, 0.345687124, 0.3788254007, 0.3972102138, 0.3260186782, 0.3302216042, 0.3378116896, 0.3352640758, 0.3368385727, 0.3590944053, 0.336264762, 0.3602395359, 0.3305424391, 0.3367194215. Close enough to 1/3 that I suspect something is happening. |
Aug 24 |
answered | The behavior of a certain greedy algorithm for Erdős Discrepancy Problem |
Aug 24 |
comment |
The behavior of a certain greedy algorithm for Erdős Discrepancy Problem
Are we requiring $f(n)$ to be $\pm 1$ only? |
Aug 14 |
answered | Duality of eta product identities: a new idea? |
Jul 19 |
awarded | Nice Answer |
Jul 19 |
comment |
Axioms for Riemann $\zeta$ function
As I stated it, yes, that is necessary. However, Kaczorowski and Perelli define what they call the extended Selberg class, where there is no Euler product, and they provide a classification of the elements of degree up to 1. Degree 0 elements are Dirichlet polynomials satisfying a certain symmetry condition, and degree 1 elements are linear combinations of the product of a degree 0 element with a (potentially shifted) Dirichlet L-function. Sound's proof also works for this class, and shows that the Dirichlet coefficients are periodic, so that multiplicativity implies Dirichlet character. |
Jul 18 |
comment |
Axioms for Riemann $\zeta$ function
Fair enough. It's also worth noting that Hamburger's theorem, as mentioned by Micah and Stopple, is the better way of stating my answer, since the conditions that the degree and conductor are 1 restrict the functional equation to being exactly the one satisfied by zeta, and is thus subject to Hamburger's result. |
Jul 18 |
answered | Axioms for Riemann $\zeta$ function |
Mar 4 |
comment |
Distinct simple zeros of Dirichlet L-functions
That is the conclusion I reached, yeah, especially after some conversations with people and a couple of failed attempts to prove something. In the application I had in mind (which actually required Artin L-functions is addition to Dirichlet), I ended up just using that it is simple to check in each case. |
Mar 4 |
accepted | Distinct simple zeros of Dirichlet L-functions |
Dec 1 |
awarded | Fanatic |
Oct 3 |
awarded | Nice Question |
Sep 20 |
awarded | Editor |