Primes, Arithmetic Functions, and the Zeta Function
2002In this chapter we will discuss properties of primes and prime decomposition in the ring A = F[T]. Much of this discussion will be facilitated by the use of the zeta function associated to A. This zeta function is an analogue of the classical zeta function which was first introduced by L.
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ABOUT THE ABSCISSA OF CONVERGENCE OF THE ZETA FUNCTION OF A MULTIPLICATIVE ARITHMETICAL SEMIGROUP
Quaestiones Mathematicae, 2001Mathematics Subject Classification (1991): 11N45 Keywords: zeta function, topological structures, algebraic structures, asymptotic, counting functions, abscissa, multiplicative arithmetical semigroup, additive arithmetical semigroup, semigroup, John Knopfmacher, radius of convergence, convergence Quaestiones Mathematicae 24(3) 2001, 363 ...
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Adelic Approach to the Zeta Function of Arithmetic Schemes in Dimension Two [PDF]
Moscow Mathematical Journal, 2008 This paper suggests a new approach to the study of the fun- damental properties of the zeta function of a model of elliptic curve over a global field. This complex valued commutative approach is a two-di- mensional extension of the classical adelic analysis of Tate and Iwasawa.
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Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields [PDF]
, 2014 In the advanced course given at Centre de Recerca Matem`atica, consisting of twelve hour lectures from 22 February to 5 March 2010, we described results and discussed some open problems regarding the gamma and zeta functions in the function field context.
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The Arithmetic of Certain Zeta Functions and Automorphic Forms on Orthogonal Groups
The Annals of Mathematics, 1980Q(z) = ,Q?(&2 of an integral weight > 0; k is a positive integer; * is an embedding of K into C; r is an element of K0 such that Id2 is its only positive conjugate; 4D-b(* + Ap) + ,cpgp, where b and c, are non-negative integers, p is the complex conjugation, and {qp} is the set of all embeddings of K into C other than * and Ap.
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ON THE ABSENCE OF ZEROS IN INFINITE ARITHMETIC PROGRESSION FOR CERTAIN ZETA FUNCTIONS
Bulletin of the Australian Mathematical Society, 2018Putnam [‘On the non-periodicity of the zeros of the Riemann zeta-function’, Amer. J. Math.76 (1954), 97–99] proved that the sequence of consecutive positive zeros of $\unicode[STIX]{x1D701}(\frac{1}{2}+it)$ does not contain any infinite arithmetic progression.
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The Arithmetic Optimization Algorithm
Computer Methods in Applied Mechanics and Engineering, 2021Laith Mohammad Abualigah +2 more
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Special Values of Zeta-Functions for Proper Regular Arithmetic Surfaces
2019We explicate Flach's and Morin's special value conjectures in [8] for proper regular arithmetic surfaces π : X → Spec Z and provide explicit formulas for the conjectural vanishing orders and leading Taylor coefficients of the associated arithmetic zeta-functions.
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MXene Ti3C2 memristor for neuromorphic behavior and decimal arithmetic operation applications
Nano Energy, 2021Jingsheng Chen, Xiaobing Yan
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A Geometric-Arithmetic Framework for the Critical Line of the Riemann Zeta Function III
We present a framework that bridges vesica piscis geometry with an arithmetic invariant to explain the critical line of the Riemann zeta function. Our approach establishes 1/2 as a fundamental invariant from two independent sources: the vesica piscis construction identifies the critical line ℜ(s) = 1/2 geometrically, while the divisor function mapping ...openaire +1 more source