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Showing 1 to 20 of 22 for “"analytic number theory"”.
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Topics in Analytic Number Theory
In the second chapter we study the Multiplicative Partition Function. In the third chapter we study an analog of the abc conjecture for arithmetical functions in r variables over a field K of characteristic zero.
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Topics in analytic number theory
This thesis, consisting of two chapters, proves several new theorems concerning L-functions and the distribution of primes. In the first chapter, we establish the first explicit form of the Vinogradov–Korobov zero-free region for Dirichlet L-functions. In the second chapter, we generalize recent …
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Topics in analytic number theory
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-09-01 without embargo terms
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Topics in analytic number theory
We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, motivated by work of Iwaniec and Sarnak, we study the question of average …
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Limit Theorems for L-functions in Analytic Number Theory
<p>We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine …
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Special Cases of Density Theorems in Algebraic Number Theory
… paper discusses the concepts in algebraic and analytic number theory used in the proofs of Dirichlet's and Cheboterev's density theorems. It presents special cases of results due to the latter theorem for which greatly simplified proofs exist.
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Weighted Universality Theorems for the Riemann and Hurwitz Zeta-Functions /
In some fields of mathematics (number theory, probability theory, mathematical statistics) weighted theorems and their applications are often investigated. Weighted universality of zeta-functions is comparatively a new branch of universality, there exist only few papers in that direction. …
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Some conditional results involving arithmetic functions
In analytic number theory, conditional results often serve as a precursor to unconditional results. In this thesis, we present two types of conditional results. First, we establish conditional estimates on twisted sums of certain arithmetic functions such as generalized von Mangoldt and Mobius …
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Laplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center
… Heisenberg groups are studied in the context of analytic number theory. Global hypoellipticty, essential self-adjointness, Sobolev spaces as well as the Sobolev estimates of the twisted bi-Laplacians are also introduced.
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Correlations of sequences modulo one and statistics of geometrical objects associated to visible points
… such sequences which behave as randomly chosen numbers from the unit interval. These include examples from the class of exponentially as well as sub-exponentially growing sequences. In the second part, we examine distribution questions for certain geometrical objects, for example, Farey-Ford and …
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Extensions of Selberg-Delange method
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 Chapter $4$, is a new identity for Multiple Zeta Values. The Selberg-Delange …
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Distribution of some arithmetic sequences
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 density functions. Next, we study the higher level correlations of these …
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Arithmetic statistics of algebraic groups
… and properties of algebraic groups of number-theoretic interest. New results obtained throughout this thesis are unified by the development and application of methods, primarily from analytic number theory, to count or bound the number of solutions to certain families of multivariate …
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Explicit Formula for the Mean Square of Dirichlet L-Functions to Prime Power Moduli
… In several important problems in analytic number theory, including how primes are distributed, estimates such as power moments provide critical input about L-functions. We derive an explicit formula for the second moment in the family of Dirichlet L- functions to a prime power …
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Topics in Multiplicative and Probabilistic Number Theory
A heuristic in analytic number theory stipulates that sets of positive integers cannot simultaneously be additively and multiplicatively structured. The practical verification of this heuristic is the source of a great number of difficult problems, including the well-known Hardy-Littlewood tuples …
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On Gaussian Multiplicative Chaos
… foundation for Kolmogorov-Obukhov-Mandelbrot theory of energy dissipation in developed turbulence. It has attracted a lot of attentions from the mathematics community in the last decade, playing a pivotal role in the probabilistic formulation of Liouville conformal field theory, as well as …
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On Some Applications of a Generalized Dwork Trace Formula to L-functions associated to Exponential Sums over Galois Rings
… and then obtain estimates on the degree (the number of zeros minus the number of poles) of the L-function (or its reciprocal) as in [Bom66] and the improvement by Adolphson and Sperber [AS87a]. We will conclude with a brief discussion on some interesting applications and extensions of this …
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