Zeta functions
Multiple zeta functions and polylogarithms over global function fields
... multiple zeta values and compare them to analogous results in the classical ...multiple zeta functions over function fields are rational functions on q −s so these formulas are expected a ...
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Laurent expansion of harmonic zeta functions
... harmonic zeta functions denoted ζ H p for each integer p ≥ 2, which are defined by the sequence of generalized harmonic numbers H p = {H (p) n } n ...
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Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results
... which contribution is larger for the small discriminants. Currently no methods are known for efficiently computing high zeros of Dedekind zeta functions of general nonabelian fields. For low zeros there is ...
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Zeta functions over zeros of Zeta functions and an exponential-asymptotic view of the Riemann Hypothesis
... for zeta functions For our later sets {w k } (all countably infinite), typical results can be categorized as: • A - Analytic structure in the whole complex x-plane (at fixed w): our zeta ...
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On the poles of topological zeta functions
... nomial f in n − 1 variables can be considered as a polynomial in n variables. An embedded resolution for f − 1 {0} ⊂ C n−1 induces the obvious analogous one for f − 1 {0} ⊂ C n = C n−1 × C and, since χ(C) = 1, the two ...
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Nested sums of symbols and renormalised multiple zeta functions
... ζ(−a 1 , −a 2 ) = lim z→0 ζ(−a 1 + z, −a 2 + z) (6) ([AET], Remark 2 therein), but this phenomenon does not survive in depth k ≥ 3. Our table does not coincide with the table given in [GZ], except at the diagonal ar- ...
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Igusa’s Local Zeta Functions and Exponential Sums for Arithmetically Non Degenerate Polynomials
... In this article we study “twisted” versions of the local zeta functions for arithmetically non-degenerate polynomials studied by Saia and Zúñiga- Galindo in [15]. Let L v be a non-Archimedean local field ...
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On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
... 2). We also refer the reader to [LK] for a recent paper dealing with upper bounds on the degrees and absolute values of the discriminants of the CM- fields of class number one, under the assumption of the generalized ...
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Asymptotic properties of Dedekind zeta functions in families of number fields
... The case s = 1 is in a sense equivalent to the Brauer–Siegel theorem so current techniques does not allow to treat it in full generality without the assumption of GRH. From now on we will assume that GRH holds for ...
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Inverse binomial series and values of Arakawa-Kaneko zeta functions
... of zeta functions of Arakawa-Kaneko-type by means of certain inverse binomial series involving harmonic sums which appeared fifteen years ago in physics in relation with the Feynman ...of zeta values ...
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On mean values of some zeta-functions in the critical strip
... [6] A. IVI0106, On zeta-functions associated with Fourier coefficients of cusp forms. Proceedings of the Amalfi Conference on Analytic Number Theory (Amalfi, September 1989), Università di Salerno, Salerno ...
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Motivic zeta functions of motives
... Theorem 1 almost provides a cycle-theoretic proof of the functional equation for the usual zeta functions of motives over finite fields. The catch is the sign conjecture. Unfortunately, the only known proof ...
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Artin formalism for Selberg zeta functions of co-finite Kleinian groups
... Selberg zeta function associated to finite area surfaces of constant negative curvature has been proved by Venkov and ...Selberg zeta; a term-by-term comparison of the spectral expansions (via trace ...
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Twisted characteristic $p$ zeta functions
... twisted zeta functions proposed in this paper are in the spirit of the twisted zeta functions ζ A (t; θ; s) defined above, the proof of the convergence of these functions, and their ...
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On systolic zeta functions
... 6. Zeta functions and isoperimetric inequalities with the length spectrum In this section we consider a closed, orientable manifold M of dimension m and first Betti number b = b 1 ...
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Renormalisation of q-Regularised Multiple Zeta Values
... Motives, volume 648 of Contemp. Math., pages 169–202. Amer. Math. Soc., Providence, RI, 2015. 23. K. Schlesinger. Some remarks on q-deformed multiple polylogarithms. arXiv:math/0111022, 2001. 24. J. Singer. On ...
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The Selberg zeta function for convex co-compact Schottky groups
... the values of Z 0 N (s)/Z N (s) used in the calculations above. Acknowledgements. The first author would like to thank J. Anderson for helpful mail dis- cussion. In addition to Curt McMullen, the third author would like ...
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Ergodic Universality Theorems for the Riemann Zeta-Function and other $L$-Functions
... universal zeta- and L-functions are Dedekind zeta- functions ζ K (s) to a number field K, L-functions associated with modular forms, and certain Hurwitz zeta-functions, to ...
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Renormalisation group for multiple zeta values
... multiple zeta values at arguments of any sign in a way that is com- patible with both the quasi-shuffle product as well as meromorphic continuation, is commonly referred to as the renormalisation problem for ...
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A sum-shuffle formula for zeta values in Tate algebras
... A sum-shuffle formula for zeta values in Tate algebras Tome 29, n o 3 (2017), p. 1025-1048. <http://jtnb.cedram.org/item?id=JTNB_2017__29_3_1025_0> © Société Arithmétique de Bordeaux, 2017, tous droits ...
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