William Craig

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All published works

Action	Title	Year	Authors
+	On the distribution of the norm of partitions	2025	Walter Bridges William Craig
+ PDF Chat	Distribution of Alternating Sums of Parts in Partitions	2025	William Craig R. Li
+	On the Asymptotic Behavior for Partitions Separated by Parity	2025	Kathrin Bringmann William Craig Caner Nazaroglu
+	The Riemann hypothesis for period polynomials of cusp forms	2025	William Craig Wissam Raji
+ PDF Chat	Precision Asymptotics for Partitions Featuring False-Indefinite Theta Functions	2024	Kathrin Bringmann William Craig Caner Nazaroglu
+	Integer partitions detect the primes	2024	William Craig Jan‐Willem van Ittersum Ken Ono
+ PDF Chat	Zero attractors of hook polynomials and related questions	2024	Walter Bridges William Craig Amanda Folsom Larry Rolen
+ PDF Chat	Distribution of hooks in self-conjugate partitions	2024	William Craig Ken Ono Ajit Singh
+ PDF Chat	On the asymptotic behavior for partitions separated by parity	2024	Kathrin Bringmann William Craig Caner Nazaroglu
+ PDF Chat	Limiting behaviour of MacMahon-like q-series	2024	Kathrin Bringmann William Craig Jan‐Willem van Ittersum Badri Vishal Pandey
+ PDF Chat	Do Numbers Exist?	2024	Peter van Inwagen William Craig
+ PDF Chat	Asymptotic equidistribution for partition statistics and topological invariants	2023	Giulia Cesana William Craig Joshua Males
+	Corrigendum to “Variants of Lehmer's speculation for newforms” [Adv. Math. 428 (2023) 109141]	2023	Jennifer S. Balakrishnan William Craig Ken Ono Wei‐Lun Tsai
+	Hook length biases and general linear partition inequalities	2023	Cristina Ballantine Hannah E. Burson William Craig Amanda Folsom Boya Wen
+ PDF Chat	Seaweed algebras and the index statistic for partitions	2023	William Craig
+ PDF Chat	Variants of Lehmer's speculation for newforms	2023	Jennifer S. Balakrishnan William Craig Ken Ono Wei‐Lun Tsai
+	Hook length biases and general linear partition inequalities	2023	Cristina Ballantine Hannah E. Burson William Craig Amanda Folsom Boya Wen
+	The Riemann Hypothesis for period polynomials of cusp forms	2023	William Craig Wissam Raij
+	On the distribution of the norm of partitions	2023	Walter Bridges William Craig
+	Asymptotics for $d$-fold partition diamonds and related infinite products	2023	Kathrin Bringmann William Craig Joshua Males
+	Inequalities and asymptotics for hook numbers in restricted partitions	2023	William Craig Madeline Locus Dawsey Guo-Niu Han
+ PDF Chat	On the number of parts in congruence classes for partitions into distinct parts	2022	William Craig
+ PDF Chat	On Ramanujan-type congruences for multiplicative functions	2022	William Craig Mircea Merca
+ PDF Chat	Distributions on partitions arising from Hilbert schemes and hook lengths	2022	Kathrin Bringmann William Craig Joshua Males Ken Ono
+	On the coefficients of $q$-series and modular forms	2022	William Craig
+ PDF Chat	On Ramanujan-type Congruences for Multiplicative Functions	2021	William Craig Mircea Merca
+ PDF Chat	Asymptotic equidistribution for partition statistics and topological invariants	2021	Giulia Cesana William Craig Joshua Males
+ PDF Chat	On the Number of Parts in Congruence Classes for Partitions into Distinct Parts	2021	William Craig
+ PDF Chat	Distribution Properties for t-Hooks in Partitions	2021	William Craig Anna Pun
+	A note on the higher order Turán inequalities for k-regular partitions	2021	William Craig Anna Pun
+	The Argument from the Applicability of Mathematics	2021	William Craig
+	On Ramanujan-type Congruences for Multiplicative Functions	2021	William Craig Mircea Merca
+	Seaweed Algebras and the Index Statistic for Partitions	2021	William Craig
+	Distributions on partitions arising from Hilbert schemes and hook lengths	2021	Kathrin Bringmann William Craig Joshua Males Ken Ono
+	Asymptotic equidistribution for partition statistics and topological invariants	2021	Giulia Cesana William Craig Joshua Males
+	On the Number of Parts in Congruence Classes for Partitions into Distinct Parts	2021	William Craig
+ PDF Chat	Unique product groups and congruence subgroups	2020	William Craig Peter A. Linnell
+	Distribution properties for t-hooks in partitions	2020	William Craig Anna Pun
+ PDF Chat	Variations of Lehmer's Conjecture for Ramanujan's tau-function	2020	Jennifer S. Balakrishnan William Craig Ken Ono
+	Unique product groups and congruence subgroups	2020	William Craig Peter A. Linnell
+	Variations of Lehmer's Conjecture for Ramanujan's tau-function	2020	Jennifer S. Balakrishnan William Craig Ken Ono
+	Distribution properties for t-hooks in partitions	2020	William Craig Anna Pun
+	Unique product groups and congruence subgroups	2020	William Craig Peter A. Linnell
+	Variants of Lehmer's speculation for newforms	2020	Jennifer S. Balakrishnan William Craig Ken Ono Wei‐Lun Tsai
+	Higher order Tur\'{a}n inequalities for $k$-regular partitions	2019	William Craig Anna Pun
+	A note on the Higher order Tur\'{a}n inequalities for $k$-regular partitions	2019	William Craig Anna Pun
+	Cubefree Trinomial Discriminants	2019	William Craig
+	A note on the Higher order Turán inequalities for $k$-regular partitions	2019	William Craig Anna Pun
+	Cubefree Trinomial Discriminants	2019	William Craig
+	Ultima Facie Interpretive Strategies	2017	William Craig
+	Pretense Theory	2017	William Craig
+	An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure	2015	William Craig
+	Methuselah’s Diary and the Finitude of the Past	2014	Ben Waters William Craig Bertrand Russell’s Tristram Shandy
+	God and Abstract Objects	2012	William Craig
+	Mathematics and Reality	2011	William Craig
+	Ferdinand Gonseth. Les Mathématiques et la réalité. Essai sur la méthode axiomatique. A reprint of II 45. Librairie scientifique et technique. Albert Blanchard, Paris1974, xi + 386 pp.	1980	William Craig
+	Review: Aubert Daigneault, Freedom in Polyadic Algebras and Two Theorems of Beth and Craig; Aubert Daigneault, On Automorphisms of Polyadic Algebras	1971	William Craig
+	Aubert Daigneault. Freedom in polyadic algebras and two theorems of Beth and Craig. The Michigan mathematical journal, vol. 11 (1964), pp. 129–135. - Aubert Daigneault. On automorphisms of polyadic algebras. Transactions of the American Mathematical Society, vol. 112 (1964), pp. 84–130.	1971	William Craig
+	Abraham Robinson. A result on consistency and its application to the theory of definition. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, Series A, vol. 59 (1956), pp. 47–58; also <b><i>Indagationes mathematicae,</i></b> vol. 18 (1956), pp. 47–58.	1960	William Craig
+	E. W. Beth. On Padoa's method in the theory of definition. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A, vol. 56 (1953), pp. 330–339; also <i><b>Indagationes mathematicae</b></i>, vol. 15 (1953), pp. 330–339.	1956	William Craig
+	Wolfram Schwabhäuser. Zur Definition des geordneten Paares von Mengen beliebiger Stufe. Mathematische Nachrichten, vol. 11 (1954), pp. 81–84.	1955	William Craig
+	Eighteenth meeting of the Association for Symbolic Logic	1955	William Craig
+	John Myhill. A derivation of number theory from ancestral theory. The journal of symbolic logic, Bd. 17 (1952), pp. 192–197.	1953	William Craig

Common Coauthors

Coauthor	Papers Together
Ken Ono	8
Anna Pun	7
Joshua Males	6
Jennifer S. Balakrishnan	5
Kathrin Bringmann	5
Amanda Folsom	3
Walter Bridges	3
Giulia Cesana	3
Wei‐Lun Tsai	3
Caner Nazaroglu	3
Peter A. Linnell	3
Mircea Merca	3
Cristina Ballantine	2
Jan-Willem van Ittersum	2
Hannah E. Burson	2
Boya Wen	2
Kathrin Bringmann	1
Madeline Locus Dawsey	1
Kathrin Bringmann	1
Ken Ono	1
Peter van Inwagen	1
Larry Rolen	1
Wissam Raji	1
Tristram Shandy	1
Ajit Singh	1
R. Li	1
Badri Vishal Pandey	1
Bertrand Russell’s	1
Wissam Raij	1
Guo-Niu Han	1
Ben Waters	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Asymptotic formulae in combinatory analysis	1918	G. H. Hardy S. Ramanujan	4
+	Integer partitions, probabilities and quantum modular forms	2017	Hieu T. Ngo Robert C. Rhoades	4
+ PDF Chat	On a Tauberian theorem of Ingham and Euler–Maclaurin summation	2021	Kathrin Bringmann Chris Jennings-Shaffer Karl Mahlburg	4
+ PDF Chat	Partitions with a restriction on the multiplicity of the summands	1971	Peter Hagis	4
+ PDF Chat	Asymptotic Formulaae in Combinatory Analysis	1918	G. H. Hardy S. Ramanujan	4
+	Une interprétation des congruences relatives à la fonction $\tau$ de Ramanujan	1968	Jean-Pierre Serre	3
+	La conjecture de Weil. I	1974	Pierre Deligne	3
+ PDF Chat	Defect zero blocks for finite simple groups	1996	Andrew Granville Ken Ono	3
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust	3
+	Representation Theory of the Symmetric Group.	1961	J. S. Frame G. de B. Robinson	3
+	The vanishing of Ramanujan’s function τ(n)	1947	D. H. Lehmer	3
+ PDF Chat	Seiberg-Witten Theory and Random Partitions	2007	Nikita Nekrasov Andreĭ Okounkov	3
+ PDF Chat	Distributions on partitions arising from Hilbert schemes and hook lengths	2022	Kathrin Bringmann William Craig Joshua Males Ken Ono	3
+ PDF Chat	Odd values of the Ramanujan $\tau$-function	1987	M. Ram Murty V. Kumar Murty T. N. Shorey	3
+ PDF Chat	Log-concavity of the partition function	2014	Stephen DeSalvo Igor Pak	3
+	On the Lebesgue-Nagell equation and related subjects	2010	Carlos Filipe Barros	3
+	Primary cyclotomic units and a proof of Catalans conjecture	2004	Preda Mihăilescu	3
+	Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary	2001	Bruce C. Berndt Ken Ono	3
+ PDF Chat	Les nombres de Lucas et Lehmer sans diviseur primitif	2006	Mourad Abouzaid	3
+ PDF Chat	On the practical solution of the Thue equation	1989	Nikos Tzanakis B.M.M. de Weger	3
+ PDF Chat	Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers	2006	Yann Bugeaud Maurice Mignotte Samir Siksek	3
+ PDF Chat	Existence of primitive divisors of Lucas and Lehmer numbers	2001	Yonatan Bilu Guillaume Hanrot Paul Voutier	3
+	The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and 𝑞-series	2003	Ken Ono	3
+ PDF Chat	Classical and modular approaches to exponential Diophantine equations II. The Lebesgue–Nagell equation	2006	Yann Bugeaud Maurice Mignotte Samir Siksek	2
+ PDF Chat	New examples of torsion-free non-unique product groups	2013	William Carter	2
+	Higher order Turán inequalities for the partition function	2018	William Chen Dennis X. Q. Jia Larry X. W. Wang	2
+	Modular Functions and Dirichlet Series in Number Theory	1990	Tom M. Apostol	2
+	Über zwei Arten von Faktorenfolgen in der Theorie der algebraischen Gleichungen.	1914	J. Schur G. PɃlya	2
+ PDF Chat	Amenable groups with a locally invariant order are locally indicable	2014	Peter A. Linnell Dave Witte Morris	2
+ PDF Chat	Congruence subgroups and the Atiyah conjecture	2006	Daniel R. Farkas Peter A. Linnell	2
+ PDF Chat	Jensen polynomials for the Riemann zeta function and other sequences	2019	Michael Griffin Ken Ono Larry Rolen Don Zagier	2
+	Torsion-free group without unique product property	1987	Eliyahu Rips Yoav Segev	2
+ PDF Chat	Hyperbolicity of the partition Jensen polynomials	2019	Hannah Larson Ian Wagner	2
+ PDF Chat	ON GEOMETRIC ASPECTS OF DIFFUSE GROUPS	2016	Jean Raimbault Steffen Kionke Nathan M. Dunfield	2
+ PDF Chat	From partitions to Hodge numbers of Hilbert schemes of surfaces	2019	Nate Gillman Xavier Gonzalez Ken Ono Larry Rolen Matthew Schoenbauer	2
+	On the Numerical Factors of the Arithmetic Forms α n ± β n	1913	R. D. Carmichael	2
+ PDF Chat	The Hook Graphs of the Symmetric Group	1954	J. S. Frame G. de B. Robinson Robert Thrall	2
+	On the Maxima and Minima of Bernoulli Polynomials	1940	D. H. Lehmer	2
+	Rips–Segev torsion-free groups without the unique product property	2015	Markus Steenbock	2
+	A Simple Example of a Torsion-Free, Non Unique Product Group	1988	S. David Promislow	2
+ PDF Chat	On the Diophantine Equation <i>n</i>(<i>n</i> + <i>d</i>) · · · (<i>n</i> + (<i>k</i> − 1)<i>d</i>) = <i>by</i><sup><i>l</i></sup>	2004	Kálmán Győry Lajos Hajdu N. Saradha	2
+	Classical and modular approaches to exponential Diophantine equations	2016	Yann Bugeaud Maurice Mignotte Samir Siksek	2
+	Solving Thue Equations of High Degree	1996	Yuri Bilu Guillaume Hanrot	2
+	Commutator subgroups of Hantzsche–Wendt groups	2007	Bartosz Putrycz	2
+ PDF Chat	Higher order Turán inequalities	1998	Dimitar K. Dimitrov	2
+ PDF Chat	Sur les entiers $N$ pour lesquels il y a beaucoup de groupes abéliens d'ordre $N$	1978	Jean-Louis Nicolas	2
+ PDF Chat	A Convergent Series for the Partition Function <i>p</i> ( <i>n</i> )	1937	Hans Rademacher	2
+	Asymptotics and Special Functions	1997	F. W. J. Olver	2
+ PDF Chat	Finite index subgroups without unique product in graphical small cancellation groups: Figure 1.	2015	D. Gruber Alexandre Martin Markus Steenbock	2
+	On an inequality of P. Turán concerning Legendre polynomials	1948	Gábor Szegő	2