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Analogies Between Function Fields and Number Fields
American Journal of Mathematics, 1983Whereas Iwasawa's theory of p-cyclotomic extensions was inspired by Weil's theory of the characteristic polynomial of the Frobenius endomorphism of a function field over a finite field of constants, the authors of the present paper in turn take Iwasawa's theory as a sample for an analogous theory in the setting of function fields resp.
Mazur, B., Wiles, A.
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Global L -functions over function fields
Mathematische Annalen, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Algebraic Function Fields and Global Function Fields
2002So far we have been working with the polynomial ring A inside the rational function field k = F(T). In this section we extend our considerations to more general function fields of transcendence degree one over a general constant field. This process is somewhat like passing from elementary number theory to algebraic number theory.
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Applicable Algebra in Engineering, Communication and Computing, 2008
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Hachenberger, D. +2 more
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Hachenberger, D. +2 more
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Superzeta functions on function fields
Finite Fields and Their ApplicationsSuperzeta functions have been studied by \textit{A. Voros} [Zeta functions over zeros of zeta functions. Berlin: Springer (2010; Zbl 1206.11106)]. More precisely, these superzeta functions consist of three types of sums which come about by summing over the zeros \(\rho\) of the Riemann zeta function \(\zeta(s)\).
Kajtaz H. Bllaca +3 more
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L-FUNCTIONS OF FUNCTION FIELDS
Number Theory, 2007This is a short expository paper on L-functions of function fields, based on the author’s lecture given at the fourth China-Japan number theory conference held in Weihai.
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Universality of L-functions over function fields
Advances in MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrade, Julio C. +2 more
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Near-field functional field transformation structures
Postconference Digest Quantum Electronics and Laser Science, 2003. QELS., 2003Irregular wavelength-scale transformation structures offer potential for wavelength division multiplexing and laser mode control. A microwave waveguide experiment demonstrates for the first time wavelength-dependent mode conversion. Optical realization using silicon processing is facilitated by lift-off.
M. Yang, J. Li, H. Chen, K.J. Webb
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2002
In the last chapter we explored the arithmetic of constant field extensions and noted (as was pointed out by Iwasawa) that these extensions can be thought of as function field analogues of cyclotomic extensions of number fields. This analogy led to various conjectures about the behavior of class groups in number fields which have proved very fruitful ...
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In the last chapter we explored the arithmetic of constant field extensions and noted (as was pointed out by Iwasawa) that these extensions can be thought of as function field analogues of cyclotomic extensions of number fields. This analogy led to various conjectures about the behavior of class groups in number fields which have proved very fruitful ...
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2018
We all know that a good way to study a mathematical subject is to give a lecture course about it. The necessity to arrange the theory in a systematic way and to explain to the audience the various connections between the different results, often leads to new insights and, in consequence, to new results.
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We all know that a good way to study a mathematical subject is to give a lecture course about it. The necessity to arrange the theory in a systematic way and to explain to the audience the various connections between the different results, often leads to new insights and, in consequence, to new results.
openaire +1 more source