Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 9 of 9 for “"Circle method"”.
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An Algebraic Circle Method
… we present an adaptation of the Hardy-Littlewood Circle Method to give estimates for the number of curves in a variety over a finite field. The key step in the classical Circle Method is to prove that some cancellation occurs in some exponential sums. Using a theorem of Katz, we reduce this to …
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Fractional parts of powers and related topics
… additive bases. The Hardy-Littlewood-Vinogradrov circle method is used with a theorem from Chapter 1 to prove a version of the Ideal Waring problem with restricted summands.
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Secondary Terms in Asymptotics for the Number of Zeros of Quadratic Forms
… O_{J,\epsilon}(B^{n/2+\epsilon-1})$. We use the circle method and work classically to exploit Gauss sums and find Dirichlet characters that fit into the odd degree case. We also provide an explicit description of the Dirichlet series arisen during the investigation, which is useful in …
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The representation of numbers as sums of unlike powers
… This is accomplished by adapting a new iterative method, developed by Vaughan and T. D. Wooley for use in Waring's problem, for problems involving mixed powers. As with the other papers on the subject, the proof employs the machinery of the Hardy-Littlewood circle method. We also consider the …
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Rademacher-Type Series
Unavailable
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Higher-order Fourier analysis with applications to additive combinatorics and theoretical computer science
… (known in this context as the Hardy-Littlewood circle method) to show that every sufficiently-large odd integer can be written as the sum of three primes, while van der Corput similarly showed that the primes contain infinitely-many three-term arithmetic progressions. Over the past two decades, …
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Terrain, Climate, and Vegetation in the Badlands of the Little Missouri River in North Dakota
… Park in a previous study are depicted using a circle method to represent azimuth and slope angle. Twelve plants are analyzed, and individual patterns emerge.</p>
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Some topics in analytic and probabilistic number theory
… of a typical integer. Our proofs use martingale methods, as well as a conditioning argument special to this problem. Next, we will prove an almost sure omega result for the sum of a random multiplicative function, substantially improving the existing result of Halasz. We will do this using a …
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Partition asymptotics; zeros of zeta functions; and Apéry-like numbers
… k, a0; and b0. Using the Hardy-Littlewood circle method, we give an asymptotic formula for the number of such partitions, thus generalizing the aforementioned results of Wright and Vaughan. We also consider the parity problem for such partitions and prove that the number of such partitions …