User:Vipul - Revision history

Vipul: /* Notes for stuff I plan to expand */

2026-08-26T00:28:07Z

Notes for stuff I plan to expand

← Older revision		Revision as of 00:28, 26 August 2026
Line 6:		Line 6:

	In [[Euler totient function]], to Measures of difference, add entries for <math>\ln (\varphi(n) / n) / \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln \ln n</math> for various <math>D</math>. I expect 0 at primes for all, and 0, 0, -1 at primorials since <math>(1 - 1/p)</math> for a primorial should have log approx <math>-\ln \ln \ln n</math>.		In [[Euler totient function]], to Measures of difference, add entries for <math>\ln (\varphi(n) / n) / \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln \ln n</math> for various <math>D</math>. I expect 0 at primes for all, and 0, 0, -1 at primorials since <math>(1 - 1/p)</math> for a primorial should have log approx <math>-\ln \ln \ln n</math>.

			===Multiplicative and completely multiplicative functions===

			* [[Multiplicative functions form abelian group under Dirichlet product]]: Characterize the group as an external direct product of countably many (prime-indexed) copies of <math>1 + xR[[x]]</math> under multiplication (a formal group law on the power series)
			* [[Multiplicative function]]: Mention the above characterization
			* [[Modified Dirichlet character]]: Make a page on these
			* [[Completely multiplicative function]]
			** Mention modified Dirichlet characters
			** Discuss their generating role in all the "interesting" parts of the group of multiplicative functions (basically, everything that shows up in our study is a finite Euler product, or a convolution of finitely many completely multiplicative functions and their inverses)

Vipul: /* Notes for stuff I plan to expand */

2026-08-25T19:19:31Z

Notes for stuff I plan to expand

← Older revision		Revision as of 19:19, 25 August 2026
Line 5:		Line 5:
	===Euler totient function===		===Euler totient function===

	In [[Euler totient function]], to Measures of difference, add entries for <math>\ln (\varphi(n) / n) / \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln n</math>, ~~<math>~~<math>\ln (\varphi(n) / n) / \ln \ln \ln n</math> for various <math>D</math>. I expect 0 at primes for all, and 0, 0, -1 at primorials since <math>(1 - 1/p)</math> for a primorial should have log approx <math>-\ln \ln \ln n</math>.		In [[Euler totient function]], to Measures of difference, add entries for <math>\ln (\varphi(n) / n) / \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln \ln n</math> for various <math>D</math>. I expect 0 at primes for all, and 0, 0, -1 at primorials since <math>(1 - 1/p)</math> for a primorial should have log approx <math>-\ln \ln \ln n</math>.

Vipul at 19:19, 25 August 2026

2026-08-25T19:19:19Z

← Older revision		Revision as of 19:19, 25 August 2026
Line 1:		Line 1:
	I'm Vipul, the person who came up with the original idea for this website.		I'm Vipul, the person who came up with the original idea for this website.

			==Notes for stuff I plan to expand==

			===Euler totient function===

			In [[Euler totient function]], to Measures of difference, add entries for <math>\ln (\varphi(n) / n) / \ln n</math>, <math>\ln (\varphi(n) / n) / \ln \ln n</math>, <math><math>\ln (\varphi(n) / n) / \ln \ln \ln n</math> for various <math>D</math>. I expect 0 at primes for all, and 0, 0, -1 at primorials since <math>(1 - 1/p)</math> for a primorial should have log approx <math>-\ln \ln \ln n</math>.

WikiSysop: Creating user page with biography of new user.

2009-03-18T22:29:23Z

Creating user page with biography of new user.

New page

I'm Vipul, the person who came up with the original idea for this website.