Editing Euler's constant (section)

===Number theory===

* An inequality for [[Euler's totient function]].<ref>{{Cite journal |last1=Rosser |first1=J. Barkley |last2=Schoenfeld |first2=Lowell |date=1962 |title=Approximate formulas for some functions of prime numbers |url=https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-6/issue-1/Approximate-formulas-for-some-functions-of-prime-numbers/10.1215/ijm/1255631807.full |journal=Illinois Journal of Mathematics |volume=6 |issue=1 |pages=64–94 |doi=10.1215/ijm/1255631807 |issn=0019-2082}}</ref>
* The growth rate of the [[divisor function]].<ref>{{Cite book |last1=Hardy |first1=Godfrey H. |title=An introduction to the theory of numbers |last2=Wright |first2=Edward M. |last3=Silverman |first3=Joseph H. |date=2008 |publisher=Oxford University Press |isbn=978-0-19-921986-5 |editor-last=Heath-Brown |editor-first=D. R. |edition=6th |series=Oxford mathematics |location=Oxford New York Auckland |page=469-471}}</ref>
* A formulation of the [[Riemann hypothesis]].<ref name=":2" /><ref>{{Cite journal |last=Robin |first=Guy |date=1984 |title=Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann |url=http://zakuski.utsa.edu/~jagy/Robin_1984.pdf |journal=Journal de mathématiques pures et appliquées |volume=63 |pages=187–213}}</ref>
* The third of [[Mertens' theorems]].*<ref name=":9" />
* The calculation of the [[Meissel–Mertens constant]].<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Mertens Constant |url=https://mathworld.wolfram.com/MertensConstant.html |access-date=2024-11-01 |website=mathworld.wolfram.com |language=en}}</ref>
* Lower bounds to specific [[Prime gap#Lower bounds|prime gaps]].<ref>{{Cite journal |last=Pintz |first=János |date=1997-04-01 |title=Very Large Gaps between Consecutive Primes |url=https://www.sciencedirect.com/science/article/pii/S0022314X97920813 |journal=Journal of Number Theory |volume=63 |issue=2 |pages=286–301 |doi=10.1006/jnth.1997.2081 |issn=0022-314X}}</ref>
* An [[approximation]] of the average number of [[Divisor|divisors]] of all numbers from 1 to a given ''n.''<ref name=":6" />
* The [[Lenstra–Pomerance–Wagstaff conjecture]] on the frequency of [[Mersenne prime|Mersenne primes]].<ref>{{Cite web |title=Heuristics: Deriving the Wagstaff Mersenne Conjecture |url=https://t5k.org/mersenne/heuristic.html |access-date=2024-11-01 |website=t5k.org}}</ref>
* An estimation of the efficiency of the [[euclidean algorithm]].<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Porter's Constant |url=https://mathworld.wolfram.com/PortersConstant.html |access-date=2024-11-01 |website=mathworld.wolfram.com |language=en}}</ref>
* Sums involving the [[Möbius function|Möbius]] and [[Von Mangoldt function|von Mangolt function]].
* Estimate of the divisor summatory function of the [[Dirichlet hyperbola method]].<ref>{{Cite book |last=Tenenbaum |first=Gérald |url=https://books.google.de/books?id=UEk-CgAAQBAJ&lpg=PR15&dq=dirichlet%20hyperbola%20method&hl=de&pg=PA360#v=onepage&q=dirichlet%20hyperbola%20method&f=false |title=Introduction to Analytic and Probabilistic Number Theory |date=2015-07-16 |publisher=American Mathematical Soc. |isbn=978-0-8218-9854-3 |language=en}}</ref>