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Showing 1 to 8 of 8 for “"Gauss sums"”.
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Explicit multiplicative relations between Gauss sums
… that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit …
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Sign Ambiguities of Gaussian Sums
… and Davenport-Hasse} relations, between Gaussian sums, were known. In 1964, H. Hasse conjectured that the norm and Davenport-Hasse relations are the only multiplicative relations connecting the Gaussian sums over $mathbb F_p$. However, in 1966, K. Yamamoto provided a simple counterexample …
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Mathematical Reasoning and the Inductive Process: An Examination of The Law of Quadratic Reciprocity
… of the first proof of this law given by Gauss. We then describe Gauss’ fourth proof of this law based on Gauss sums, followed by a look at Eisenstein’s geometric simplification of Gauss’ third proof. Finally, we finish with an examination of one of the modern proofs of this theorem …
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Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula
… -function and an Dirichlet series defined using Gauss sums, in order to demonstrate the arithmetic content. In this paper we reexamine this connection in the particular case that was discussed in Metaplectic Forms. By looking through the scope of twisted multiplicativity, a property of L-series, …
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Identities involving theta functions and analogues of theta functions
… various generalized two-dimensional lattice sums, one of which arose from the solution to a certain Poisson equation. We evaluate certain lattice sums in closed form using results from Ramanujan's theory of theta functions, continued fractions and class invariants. Many nice explicit examples …
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Secondary Terms in Asymptotics for the Number of Zeros of Quadratic Forms
… 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 applications. It turns out that the geometric …
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On Some Applications of a Generalized Dwork Trace Formula to L-functions associated to Exponential Sums over Galois Rings
… trace formula that applies to exponential sums over Galois rings and the associated L-function. Using the generalized trace formula, we will prove more results on the L-function, analogous to the classical results by Dwork and Bombieri who studied L-functions associated to such exponential …
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Talbotův jev
… v prostredí Python: analytický model využívajúci Gaussove sumy a numerický model založený na metóde uhlového spektra (ASM). Správnosť oboch algoritmov bola overená priamym porovnaním nasimulovaných dát s reálnymi difrakčnými obrazcami z CCD kamery v rôznych fázových vzdialenostiach. Výsledky na …