User contributions for Maxieds

8 July 2021

• 22:2622:26, 8 July 2021 diff hist +32 Mertens function →As an integral: By my understanding, \rho is complex-valued where as we require the values of M(x) to be at least real-valued. This seems to be a common in source some references on M(x) that cite the formula in Titchmarsh verbatim. I believe there should be a real part taken along those points of complex exponentiation... Let me know if I'm off on this. Tag: Reverted

23 March 2021

• 20:5820:58, 23 March 2021 diff hist +275 Prime omega function →Dirichlet series
• 20:5420:54, 23 March 2021 diff hist +36 m Prime omega function →Average order and summatory functions

6 March 2021

• 23:2323:23, 6 March 2021 diff hist +742 Talk:Power (physics) →Improving the Radiant power section: new section
• 12:5112:51, 6 March 2021 diff hist +423 Dirichlet series →Coefficient inversion (integral formula)

28 February 2021

• 23:2723:27, 28 February 2021 diff hist +1,454 Talk:Criticism of Linux →On the observation of degradation of quality of OSS over the years: new section Tag: Reverted

15 October 2020

• 05:2205:22, 15 October 2020 diff hist +89 Prime omega function →Properties and relations: A curious identity proved via DGFs
• 05:1805:18, 15 October 2020 diff hist +74 m Prime omega function →Properties and relations: Adding a new identity cited in "A catalog of interesting and useful Lambert series identities"

9 October 2020

• 19:3619:36, 9 October 2020 diff hist +58 Determinant →Relation to eigenvalues and trace: The cited formula from the reference has unclear specification of the conditions on the indices before this change. Compare to the Newton

4 July 2020

• 03:5403:54, 4 July 2020 diff hist +941 Möbius inversion formula →Generalizations: Moving misplaced identities.
• 03:5303:53, 4 July 2020 diff hist −1,198 Möbius inversion formula →Statement of the formula: Moving the series formulas to the generalizations section.
• 03:5103:51, 4 July 2020 diff hist +1,405 Möbius inversion formula →Statement of the formula: There were several important variants missing. Namely, the product form of Mobius inversion. Also, adding references where not cited in the later sections.

3 July 2020

• 02:1002:10, 3 July 2020 diff hist +50 m Prime omega function →Dirichlet series

30 April 2020

• 06:0406:04, 30 April 2020 diff hist +305 User talk:LadyofShalott Looking for deleted page contents
• 06:0106:01, 30 April 2020 diff hist +353 User talk:Clpo13 Looking for deleted data on 2600 hacker

27 April 2020

• 22:1622:16, 27 April 2020 diff hist +254 m Dirichlet convolution →Examples
• 22:1122:11, 27 April 2020 diff hist +157 Prime omega function →Dirichlet series: Adding DGF identities from Section 1.3 of Montgomery and Vaughan (exercises)

1 March 2020

• 22:3022:30, 1 March 2020 diff hist 0 m Lambert series →Recurrence relations
• 10:1310:13, 1 March 2020 diff hist +9 m Lambert series →Examples
• 08:0508:05, 1 March 2020 diff hist −43 Lambert series →Examples: This correction needs to be made.

25 February 2020

• 21:3621:36, 25 February 2020 diff hist +188 Prime omega function →Dirichlet series: Found an application for this Dirichket series -- adding it as an example of the lemma

9 December 2019

• 20:0920:09, 9 December 2019 diff hist +551 List of RNA structure prediction software →Secondary structure viewers, editors: Shameless plug for the gtDMMB organization source code I have been developing under the direction of Professor Christine Heitsch's group at GA Tech.

2 October 2019

• 20:1720:17, 2 October 2019 diff hist +3,958 Dirichlet series →Examples: Had to add some (compendia in some cases) missing details to the page. That which is not cited explicitly, is found in Apostol's book (including exercises).
• 19:2919:29, 2 October 2019 diff hist +2,039 Dirichlet series Added coefficient inversion identity, and Mellin transform identity from the summatory function of f (both are found in Chapter 11 of Apostol's book, already cited on this page)

25 September 2019

• 05:5705:57, 25 September 2019 diff hist +436 Dirichlet convolution →Dirichlet inverse: Cleaned up the cluttered structure of the section; Added a partition-based expression for the Dirichlet inverse function;

24 September 2019

• 10:4810:48, 24 September 2019 diff hist +1,447 Prime zeta function →Almost-prime zeta functions: Obligatory follow-up on how to obtain (and then generalize) the identities for these functions found in https://brilliant.org/wiki/prime-zeta-function/.
• 07:5107:51, 24 September 2019 diff hist +273 Analytic continuation →Example II: An interpretation of F as the summatory function for some arithmetic sequence
• 07:3907:39, 24 September 2019 diff hist +294 Dirichlet series inversion Restoring prior edits
• 06:5306:53, 24 September 2019 diff hist +197 User talk:Maxieds →Dirichlet series inversion moved to draftspace
• 05:5905:59, 24 September 2019 diff hist +19 m Dirichlet series inversion →Special cases of the formula
• 05:4605:46, 24 September 2019 diff hist +12,731 N Dirichlet series inversion This new page technically belongs in a sandbox -- Still working on it -- Creating a compendia of useful (and/or practical) formulas related to integral formulas for Dirichlet series (DGF) coefficient-wise inversion formulas...
• 02:1702:17, 24 September 2019 diff hist +13,032 Analytic continuation This theorem is useful, and not stated anywhere on this page already -- added the hypotheses of the theorem, theorem conclusion, and a couple of motivating example cases

23 September 2019

• 22:0222:02, 23 September 2019 diff hist +5,028 Analytic continuation →Natural boundary: Added two semi-prototypical examples of functions with natural boundaries -- makes the point about special cases where we are not able to analytically continue a complex function beyond a certain region of the plane...

15 September 2019

• 03:3703:37, 15 September 2019 diff hist +914 Dirichlet convolution →Examples: Characteristic function for the primes has a divisor sum identity -- added it

29 June 2019

• 19:1819:18, 29 June 2019 diff hist +7 Bell polynomials →Generating function: I believe that this ordering of the indices is what was meant ... The index n>=1 should not be finite.

3 June 2019

• 05:3005:30, 3 June 2019 diff hist +83 m Additive function →See also
• 05:2905:29, 3 June 2019 diff hist +963 Additive function →Summatory functions: More content from I&K book
• 05:1605:16, 3 June 2019 diff hist +1,133 Additive function Added summatory functions stats for additive functions + reference cited

2 June 2019

• 23:0123:01, 2 June 2019 diff hist +156 Möbius function →Mathematical series: Added Lambert series identity from Merca and Schmidt (2018, Ramanujan Journal) article
• 21:1121:11, 2 June 2019 diff hist +763 Prime omega function Moved Dirichlet series identity to new section; Added identity on characteristic function of the primes by a convolution.
• 08:1808:18, 2 June 2019 diff hist +1,436 Prime omega function Dirichlet series for (these) additive functions
• 07:4907:49, 2 June 2019 diff hist +970 Talk:Prime omega function Summary of why removed tag on the main page
• 07:4607:46, 2 June 2019 diff hist +106 m Prime omega function →Average order and summatory functions

25 February 2019

• 20:5320:53, 25 February 2019 diff hist +687 User talk:Maxieds →Lambert Series

28 January 2019

• 06:4906:49, 28 January 2019 diff hist +1,517 User talk:Maxieds →Lambert Series: (Response to questions ... Please log in so I can see your actual username)

13 December 2018

• 00:5500:55, 13 December 2018 diff hist +368 Redheffer matrix →Applications and generalizations
• 00:0000:00, 13 December 2018 diff hist +15 m Redheffer matrix →Matrix products expanding Dirichlet convolutions and Dirichlet inverses

12 December 2018

• 23:5023:50, 12 December 2018 diff hist +147 Redheffer matrix →Matrix products expanding Dirichlet convolutions and Dirichlet inverses
• 22:4822:48, 12 December 2018 diff hist +563 Redheffer matrix →Applications and generalizations: Cited related inversion of transforms
• 22:4222:42, 12 December 2018 diff hist +15,150 Redheffer matrix Added generalizations, including many citations; Before objecting editors should please be open minded about this interpretation of (0,1)-matrices, of which Redheffers are a significant special case -- and make sure to consider all of the recent literature which seems to suggest that this content be unified in a single article here :)