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 7 of 7 for “"squarefree"”.
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THE EFFECTIVE SATO-TATE CONJECTURE AND DENSITIES PERTAINING TO LEHMER-TYPE QUESTIONS
… Conjecture for newforms f(z) on Gamma_0(N) with squarefree level. This result assumes that the symmetric power L-functions of f(z) are automorphic and satisfy the Generalized Riemann Hypothesis. We use this result to compute the density of positive integers n for which the n-th Fourier …
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Solutions of the Cubic Fermat Equation in Quadratic Fields
… + y^3 = z^3$ in $\mathbb{Q}(\sqrt{d})$ for a squarefree integer $d$. In this variation of Fermat's Last Theorem, it is possible for nontrivial solutions to exist in $\mathbb{Q}(\sqrt{d})$ for some choices of $d$, but not for all. Our argument assumes the Birch and Swinnerton-Dyer conjecture …
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Arithmetic statistics and Vinberg representations
… first one, we obtain a result on the density of squarefree values of certain discriminant polynomials. It is conjectured that such a density should be equal to the product of local densities, but this result is only known assuming the $abc$ conjecture. We build on a result of …
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Number-theoretic properties of the binomial distribution with applications in arithmetic geometry
… certain properties, such as being prime or being squarefree. Finally, we show how to apply such a theorem, concerning a property P, to yield results concerning the probability that the numbers of points on random complete intersections possess property P.
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Combinatorial aspects of root lattices and words
… lower bounds for the entropy of ternary squarefree, binary cubefree and ternary minimally repetitive words are confirmed exactly.
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Unique Signed Minimal Wiring Diagrams and the Stanley-Reisner Correspondence
… provides a one-to-one correspondence between squarefree monomial ideals and abstract simplicial complexes. In this work, we use this correspondence to determine conditions under which a given set of inputs is guaranteed to have a unique signed minimal wiring diagram, regardless of the output …
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K-theoretic Schubert calculus and applications
… and E. Miller, and moreover in a stronger 'squarefree' form that resolves an issue raised by A. Knutson. Our work is based on the combinatorics of genomic tableaux, which we introduce, and a generalization of M.-P. Schuetzenberger's jeu de taquin. We further apply genomic tableaux to obtain …