# Browse Dissertations and Theses - Mathematics by Contributor "Zaharescu, Alexandru"

• (2017-04-05)
This thesis explores three main topics in the application of ergodic theory and dynamical systems to equidistribution and spacing statistics in number theory. The first is concerned with utilizing the ergodic properties ...

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• (2010-05-14)
Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic ...

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• (2014-09-16)
K.T. Atanassov introduced the two arithmetic functions $I(n) = \prod_{\nu=1}^k p_\nu^{1/\alpha_\nu} \qquad \text{and}\qquad R(n) = \prod_{\nu=1}^k p_\nu^{\alpha_v - 1}$ called the irrational factor and the strong ...

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• (2012-09-18)
This dissertation is divided into three main sections. The main result of Section 1 is that, for $a,b>1$, irrational, the quantity $\log (a/b)$ is not too far'' from the series of fractional parts  \sum_{n=1}^{\i ...

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• (2018-04-02)
In the first part of this thesis, we show that a wide range of the properties of the roots of translated Chebyshev polynomials of the first kind (call these complex numbers Chebyshev points), are illuminated by the study ...

application/pdf PDF (849kB) • (2010-05-19)
We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the ...

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• (2017-07-10)
This thesis is divided into two major topics. In the first, we study the topic of distribution of sequences modulo one. In particular, we look at the spacing distributions between members of rational valued sequences modulo ...

application/pdf PDF (2MB) • (2014-09-16)
This thesis is centered around three topics: the theory of the cubic theta functions as functions of two analytic variables, cubic modular equations, and a class of two-variable cubic modular equations. Chapter 2 is ...

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• (2012-09-18)
This research centers on discriminants and how discriminants and their q-analogues relate to the root distribution of polynomials. This topic includes the connections between the root distribution of a sequence of polynomials ...

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• (2007)
By Weyl's criterion the distribution of a given sequence is uniform if and only if certain exponential sums are small. For the Farey series FQ of fractions in their lowest terms with denominators not exceeding some bound ...

application/pdf PDF (2MB) • (2007)
As an most interesting example for the elliptic curve E n : y2 = x 3 - n2x, which is closely related with the congruent number problem, we study the distribution of the size of the six Selmer groups arising from the three ...

application/pdf PDF (2MB) • (2013-08-22)
In this thesis, we first study the correlations of some arithmetic sequences. We prove the existence of the limiting pair correlations of fractions with prime and power denominators, and give the explicit pair correlation ...

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• (2014-05-30)
In this work, we prove effective decay of certain multiple correlation coefficients for Weyl chamber actions of semidirect products of semisimple groups with $G$-vector spaces. Using these estimates we get decay for ...

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• (2013-05-24)
We improve the error term in the van der Corput transform for exponential sums, \sum g(n) exp(2 \pi i f(n)). For many smooth functions g and f, we can show that the largest factor of the error term is given by a simple ...

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• (2015-04-03)
This dissertation involves two topics in analytic number theory. The first topic focuses on extensions of the Selberg-Delange Method, which are discussed in Chapters $2$ and $3$. The last topic, which is discussed in ...

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• (2018-06-01)
The value distribution of the Riemann zeta function $\zeta(s)$ is a classical question. Despite the fact that values of $\zeta(s)$ are approximately Gaussian distributed, $\zeta(s)$ can be very large for infinitely many ...

application/pdf PDF (627kB) • (2013-08-22)
My dissertation is mainly about various identities involving theta functions and analogues of theta functions. In Chapter 1, we give a completely elementary proof of Ramanujan's circular summation formula of theta functions ...

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• (2009)
Finally, we describe methods to compute the divisor class number, h, of K, and in the case that O has unit rank 1 or 2, the regulator and ideal class number of O as well. A method of Scheidler and Stein [SS07, SS08] ...

application/pdf PDF (4MB) • (2012-02-01)
In this thesis, we prove several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered by Somos and establish applications of some of them. ...

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• (2012-09-18)
In this thesis, we study congruence function fields, in particular those with many rational places. This thesis consists of three parts, the first two parts present our results in two different aspects of function fields ...

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