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Articles 1 - 4 of 4
Full-Text Articles in Number Theory
Calculating Infinite Series Using Parseval's Identity, James R. Poulin
Calculating Infinite Series Using Parseval's Identity, James R. Poulin
Electronic Theses and Dissertations
Parseval's identity is an equality from Fourier analysis that relates an infinite series over the integers to an integral over an interval, which can be used to evaluate the exact value of some classes of infinite series. We compute the exact value of the Riemann zeta function at the positive even integers using the identity, and then we use it to compute the exact value of an infinite series whose summand is a rational function summable over the integers.
Statistical Mechanics Of Farey Fraction Spin Chain Models, Jan Fiala
Statistical Mechanics Of Farey Fraction Spin Chain Models, Jan Fiala
Electronic Theses and Dissertations
This thesis considers several statistical models defined on the Farey fractions. Two of these models, considered first, may be regarded as "spin chains", with long-range interactions, another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle-Perron-F'robenius operator), which is defined using the maps (presentation functions) generating the Farey "tree". The spectrum of this operator was completely determined by Prellberg. It follows that all these models have a second-order phase transition with a specific …
The Distribution Of The Irreducibles In An Algebraic Number Field, Rebecca Rozario
The Distribution Of The Irreducibles In An Algebraic Number Field, Rebecca Rozario
Electronic Theses and Dissertations
The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).
An Elementary Proof Of The Prime Number Theorem, James G. Huard
An Elementary Proof Of The Prime Number Theorem, James G. Huard
Honors College
No abstract provided.