817 reputation
1611
bio website stanford.edu/~rjlo
location Palo Alto, CA
age
visits member for 4 years, 4 months
seen 9 hours ago

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