Dyson's transform is a fundamental technique in additive number theory, it was developed by Freeman Dyson as part of his proof of which theorem?
Mann's
Title: Erdős–Tetali theorem
Passage: In additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive basis of every order.  More specifically, it states that for every fixed integer formula_1, there exists a subset of the natural numbers formula_2 satisfyingformula_3where formula_4 denotes the number of ways that a natural number "n" can be expressed as the sum of "h" elements of "B."
Title: Dyson sphere
Passage: A Dyson sphere is a hypothetical megastructure that completely encompasses a star and captures most or all of its power output.  The first known mention of the concept of a star enclosed by a sphere was in an early Indo-European religious creation myth which described the prenatal sun as being enclosed (imprisoned) by rock.  The first contemporary description of the structure was by Olaf Stapledon in his science fiction novel "Star Maker" (1937), in which he described "worlds constructed of a series of concentric spheres" and a similar galactic-scale natural formation of a "rocky sphere that had once been a galaxy."  The concept was later popularized by Freeman Dyson in his 1960 paper "Search for Artificial Stellar Sources of Infrared Radiation".  Dyson speculated that such structures would be the logical consequence of the escalating energy needs of a technological civilization and would be a necessity for its long-term survival.  He proposed that searching for such structures could lead to the detection of advanced, intelligent extraterrestrial life.  Different types of Dyson spheres and their energy-harvesting ability would correspond to levels of technological advancement on the Kardashev scale.
Title: Additive number theory
Passage: In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition.  More abstractly, the field of "additive number theory" includes the study of abelian groups and commutative semigroups with an operation of addition.  Additive number theory has close ties to combinatorial number theory and the geometry of numbers.  Two principal objects of study are the sumset of two subsets "A" and "B" of elements from an abelian group "G",
Title: Analytic number theory
Passage: In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.  It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Dirichlet "L"-functions to give the first proof of Dirichlet's theorem on arithmetic progressions.  It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem).
Title: New York Number Theory Seminar
Passage: The New York Number Theory Seminar is a research seminar devoted to the theory of numbers and related parts of mathematics and physics.  In 1981, Number Theorists Harvey Cohn, David Chudnovsky, Gregory Chudnovsky and Melvyn B. Nathanson, who were then affiliated with City College (CUNY), Columbia University, and Rutgers–Newark, and currently at Lehman College (CUNY) and the Polytechnic University of New York, began to meet regularly, usually on Thursday afternoons, during the academic year at the Graduate Center of the City University of New York.  The location was convenient to all parts of the city and major transportation hubs.  Harvey Cohn has retired, but Nathanson is now based in the City University and acts as the host of the seminar.  The New York Number Theory Seminar also organizes an annual Workshop on Combinatorial and Additive Number Theory (CANT) at the CUNY Graduate Center.  Proceedings of the seminar have been published regularly by Springer-Verlag.
Title: Crank of a partition
Passage: In number theory, the crank of a partition of an integer is a certain integer associated with the partition.  The term was first introduced without a definition by Freeman Dyson in a 1944 paper published in Eureka, a journal published by the Mathematics Society of Cambridge University.  Dyson then gave a list of properties this yet-to-be-defined quantity should have.  In 1988, George E. Andrews and Frank Garvan discovered a definition for the crank satisfying the properties hypothesized for it by Dyson.
Title: Erdős–Fuchs theorem
Passage: In mathematics, in the area of additive number theory, the Erdős–Fuchs theorem is a statement about the number of ways that numbers can be represented as a sum of two elements of a given set, stating that the average order of this number cannot be too close of being a linear function.
Title: Astrochicken
Passage: Astrochicken is the name given to a thought experiment expounded by theoretical physicist Freeman Dyson.  In his book "Disturbing the Universe" (1979), Dyson contemplated how humanity could build a small, self-replicating automaton that could explore space more efficiently than a manned craft could.  He attributed the general idea to John von Neumann, based on a lecture von Neumann gave in 1948 titled "The General and Logical Theory of Automata".  Dyson expanded on von Neumann's automata theories and added a biological component to them.
Title: Dyson's transform
Passage: Dyson's transform is a fundamental technique in additive number theory.  It was developed by Freeman Dyson as part of his proof of Mann's theorem, is used to prove such fundamental results of Additive Number Theory as the Cauchy-Davenport theorem, and was used by Olivier Ramaré in his work on the Goldbach conjecture that proved that every even integer is the sum of at most 6 primes.  The term "Dyson's transform" for this technique is used by Ramaré.  Halberstam and Roth call it the τ-transformation.
Title: Freeman Dyson
Passage: Freeman John Dyson {'1': ", '2': ", '3': ", '4': "} (born 15 December 1923) is an English-born American theoretical physicist and mathematician.  He is known for his work in quantum electrodynamics, solid-state physics, astronomy and nuclear engineering.  He theorized several concepts that bear his name, such as Dyson's transform, Dyson tree, Dyson series, and Dyson sphere.
Dyson's transform Freeman Dyson