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Journal articles on the topic 'Zeta de Dedekind'

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Published: 17 September 2021

Last updated: 6 February 2022

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1

Lu, Hongwen, Rongzheng Jiao, and Chungang Ji. "Dedekind zeta-functions and Dedekind sums." Science in China Series A: Mathematics 45, no. 8 (August 2002): 1059–65. http://dx.doi.org/10.1007/bf02879989.

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2

陆, 洪文, 春岗纪, and 荣政焦. "Dedekind zeta函数与Dedekind和." Science in China Series A-Mathematics (in Chinese) 31, no. 12 (December 1, 2001): 1057–64. http://dx.doi.org/10.1360/za2001-31-12-1057.

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3

Fomenko, O. M. "On the Dedekind Zeta Function." Journal of Mathematical Sciences 200, no. 5 (July 1, 2014): 624–31. http://dx.doi.org/10.1007/s10958-014-1952-6.

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4

KIM, TAEKYUN. "NOTE ON q-DEDEKIND-TYPE SUMS RELATED TO q-EULER POLYNOMIALS." Glasgow Mathematical Journal 54, no. 1 (December 9, 2011): 121–25. http://dx.doi.org/10.1017/s0017089511000450.

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AbstractRecently, q-Dedekind-type sums related to q-zeta function and basic L-series are studied by Simsek in [13] (Y. Simsek, q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl. 318 (2006), 333–351) and Dedekind-type sums related to Euler numbers and polynomials are introduced in the previous paper [11] (T. Kim, Note on Dedekind type DC sums, Adv. Stud. Contem. Math. 18 (2009), 249–260). It is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of the higher order Dedekind the type sums related to q-Euler polynomials and numbers by using an invariant p-adic q-integrals.

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5

Jiao, Rongzheng, and Hongwen Lu. "Dedekind zeta functions of certain real quadratic fields." Tamkang Journal of Mathematics 37, no. 4 (December 31, 2006): 367–75. http://dx.doi.org/10.5556/j.tkjm.37.2006.150.

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Using analytic and modular transformation methods, we represent the value of the product of two Dedekind zeta functions of certain real quadratic number fields at $-3$ by Dedekind sums of high rank in this paper.

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6

CHO, PETER J., and HENRY H. KIM. "Extreme residues of Dedekind zeta functions." Mathematical Proceedings of the Cambridge Philosophical Society 163, no. 2 (February 15, 2017): 369–80. http://dx.doi.org/10.1017/s0305004117000019.

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AbstractIn a family ofSd+1-fields (d= 2, 3, 4), we obtain the conjectured upper and lower bounds of the residues of Dedekind zeta functions except for a density zero set. ForS5-fields, we need to assume the strong Artin conjecture. We also show that there exists an infinite family of number fields with the upper and lower bounds, resp.

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7

Louboutin, Stéphane R. "Simple zeros of Dedekind zeta functions." Functiones et Approximatio Commentarii Mathematici 56, no. 1 (March 2017): 109–16. http://dx.doi.org/10.7169/facm/1598.

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8

Browkin, Jerzy. "Multiple zeros of Dedekind zeta functions." Functiones et Approximatio Commentarii Mathematici 49, no. 2 (December 2013): 383–90. http://dx.doi.org/10.7169/facm/2013.49.2.15.

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9

Louboutin, Stéphane R. "Real zeros of Dedekind zeta functions." International Journal of Number Theory 11, no. 03 (March 31, 2015): 843–48. http://dx.doi.org/10.1142/s1793042115500463.

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Building on Stechkin and Kadiri's ideas we derive an explicit zero-free region of the real axis for Dedekind zeta functions of number fields. We then explain how this new region enables us to improve upon the previously known explicit lower bounds for class numbers of number fields and relative class numbers of CM-fields.

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10

Fomenko, O. M. "On the Dedekind Zeta Function. II." Journal of Mathematical Sciences 207, no. 6 (May 19, 2015): 923–33. http://dx.doi.org/10.1007/s10958-015-2415-4.

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11

Bayad, Abdelmejid, and Yilmaz Simsek. "Multiple Dedekind Type Sums and Their Related Zeta Functions." Mathematics 9, no. 15 (July 24, 2021): 1744. http://dx.doi.org/10.3390/math9151744.

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The main purpose of this paper is to use the multiple twisted Bernoulli polynomials and their interpolation functions to construct multiple twisted Dedekind type sums. We investigate some properties of these sums. By use of the properties of multiple twisted zeta functions and the Bernoulli functions involving the Bernoulli polynomials, we derive reciprocity laws of these sums. Further developments and observations on these new Dedekind type sums are given.

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12

Balakrishnan, U. "Extreme values of the Dedekind zeta function." Acta Arithmetica 46, no. 3 (1986): 199–209. http://dx.doi.org/10.4064/aa-46-3-199-209.

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13

Grenié, Loïc, and Giuseppe Molteni. "Zeros of Dedekind zeta functions under GRH." Mathematics of Computation 85, no. 299 (October 9, 2015): 1503–22. http://dx.doi.org/10.1090/mcom/3024.

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14

Masri, Riad. "Multiple Dedekind zeta functions and evaluations of extended multiple zeta values." Journal of Number Theory 115, no. 2 (December 2005): 295–309. http://dx.doi.org/10.1016/j.jnt.2004.12.010.

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15

HEAP, WINSTON. "THE TWISTED SECOND MOMENT OF THE DEDEKIND ZETA FUNCTION OF A QUADRATIC FIELD." International Journal of Number Theory 10, no. 01 (January 22, 2014): 235–81. http://dx.doi.org/10.1142/s1793042113500917.

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We compute the second moment of the Dedekind zeta function of a quadratic field times an arbitrary Dirichlet polynomial of length T1/11-∊. Our result generalizes a formula of Hughes and Young concerning the fourth moment of the Riemann zeta function.

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16

LI, XIAN-JIN. "ON THE EULER PRODUCT OF THE DEDEKIND ZETA FUNCTION." International Journal of Number Theory 05, no. 02 (March 2009): 293–301. http://dx.doi.org/10.1142/s1793042109002109.

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It is well known that the Euler product formula for the Riemann zeta function ζ(s) is still valid for ℜ(s) = 1 and s ≠ 1. In this paper, we extend this result to zeta functions of number fields. In particular, we show that the Dedekind zeta function ζk(s) for any algebraic number field k can be written as the Euler product on the line ℜ(s) = 1 except at the point s = 1. As a corollary, we obtain the Euler product formula on the line ℜ(s) = 1 for Dirichlet L-functions L(s, χ) of real characters.

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17

Kadiri, Habiba, and Nathan Ng. "Explicit zero density theorems for Dedekind zeta functions." Journal of Number Theory 132, no. 4 (April 2012): 748–75. http://dx.doi.org/10.1016/j.jnt.2011.09.002.

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18

Belabas, Karim, and Eduardo Friedman. "Computing the residue of the Dedekind zeta function." Mathematics of Computation 84, no. 291 (May 7, 2014): 357–69. http://dx.doi.org/10.1090/s0025-5718-2014-02843-3.

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19

Horozov, Ivan. "Double shuffle relations for multiple Dedekind zeta values." Acta Arithmetica 180, no. 3 (2017): 201–27. http://dx.doi.org/10.4064/aa7945-8-2016.

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20

KADIRI, HABIBA. "EXPLICIT ZERO-FREE REGIONS FOR DEDEKIND ZETA FUNCTIONS." International Journal of Number Theory 08, no. 01 (February 2012): 125–47. http://dx.doi.org/10.1142/s1793042112500078.

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Let K be a number field, nK be its degree, and dK be the absolute value of its discriminant. We prove that, if dK is sufficiently large, then the Dedekind zeta function ζK(s) has no zeros in the region: [Formula: see text], [Formula: see text], where log M = 12.55 log dK + 9.69nK log |ℑ𝔪 s| + 3.03 nK + 58.63. Moreover, it has at most one zero in the region:[Formula: see text], [Formula: see text]. This zero if it exists is simple and is real. This argument also improves a result of Stark by a factor of 2: ζK(s) has at most one zero in the region [Formula: see text], [Formula: see text].

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21

Fomenko, O. M. "Mean values connected with the Dedekind zeta function." Journal of Mathematical Sciences 150, no. 3 (April 2008): 2115–22. http://dx.doi.org/10.1007/s10958-008-0126-9.

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22

Brown, Francis C. S. "Dedekind zeta motives for totally real number fields." Inventiones mathematicae 194, no. 2 (January 5, 2013): 257–311. http://dx.doi.org/10.1007/s00222-012-0444-x.

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23

Hu, Guangwei, and Ke Wang. "Higher moment of coefficients of Dedekind zeta function." Frontiers of Mathematics in China 15, no. 1 (February 2020): 57–67. http://dx.doi.org/10.1007/s11464-020-0816-2.

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24

Li, H. Y., B. Maji, and T. Kuzumaki. "A Generalization of the Secant Zeta Function as a Lambert Series." Mathematical Problems in Engineering 2020 (April 30, 2020): 1–20. http://dx.doi.org/10.1155/2020/7923671.

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Recently, Lalín, Rodrigue, and Rogers have studied the secant zeta function and its convergence. They found many interesting values of the secant zeta function at some particular quadratic irrational numbers. They also gave modular transformation properties of the secant zeta function. In this paper, we generalized secant zeta function as a Lambert series and proved a result for the Lambert series, from which the main result of Lalín et al. follows as a corollary, using the theory of generalized Dedekind eta-function, developed by Lewittes, Berndt, and Arakawa.

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25

Breuning, Manuel, and David Burns. "Leading terms of Artin L-functions at s=0 and s=1." Compositio Mathematica 143, no. 6 (November 2007): 1427–64. http://dx.doi.org/10.1112/s0010437x07002874.

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AbstractWe formulate an explicit conjecture for the leading term at s=1 of the equivariant Dedekind zeta-function that is associated to a Galois extension of number fields. We show that this conjecture refines well-known conjectures of Stark and Chinburg, and we use the functional equation of the zeta-function to compare it to a natural conjecture for the leading term at s=0.

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26

KATAYAMA, Koji. "Barnes' Multiple Zeta Function and Apostol's Generalized Dedekind Sum." Tokyo Journal of Mathematics 27, no. 1 (June 2004): 57–74. http://dx.doi.org/10.3836/tjm/1244208474.

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27

R. Louboutin, Stéphane. "Explicit Upper Bounds for Residues of Dedekind Zeta Functions." Moscow Mathematical Journal 15, no. 4 (2015): 727–40. http://dx.doi.org/10.17323/1609-4514-2015-15-4-727-740.

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28

Tollis, Emmanuel. "Zeros of Dedekind zeta functions in the critical strip." Mathematics of Computation 66, no. 219 (July 1, 1997): 1295–322. http://dx.doi.org/10.1090/s0025-5718-97-00871-5.

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29

Zagier, Don. "Hyperbolic manifolds and special values of Dedekind zeta-functions." Inventiones Mathematicae 83, no. 2 (June 1986): 285–301. http://dx.doi.org/10.1007/bf01388964.

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30

Perlis, Robert. "On the Analytic Determination of the Trace Form." Canadian Mathematical Bulletin 28, no. 4 (December 1, 1985): 422–30. http://dx.doi.org/10.4153/cmb-1985-051-2.

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AbstractThe Dedekind zeta function of an algebraic number field E determines the rational equivalence class of the trace form of E. The Hasse symbols of the trace form are related to the local Artin root numbers of the zeta function by formulas of Serre and Deligne. This is used to settle the question of which families of complex numbers appear as the local Artin root numbers of a continuous real representation of the absolute Galois group of ℚ.

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31

Elizalde, Emilio, Klaus Kirsten, Nicolas Robles, and Floyd Williams. "Zeta functions on tori using contour integration." International Journal of Geometric Methods in Modern Physics 12, no. 02 (January 29, 2015): 1550019. http://dx.doi.org/10.1142/s021988781550019x.

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A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

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32

Liang, Xiao Yu, and Xin Zhang. "Very Exceptional Group." Advanced Materials Research 1006-1007 (August 2014): 1071–75. http://dx.doi.org/10.4028/www.scientific.net/amr.1006-1007.1071.

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<p>A finite group is called exceptional if for a Galois extension of number fields with the Galois groups , the zeta function of between and does not appear in the Brauer-Kuroda relation of the Dedekind zeta functions. Furthermore, a finite group is called very exceptional if its nontrivial subgroups are all exceptional. In this paper，a Nilpotent group is very exceptional if and only if it has a unique subgroup of prime order for each divisor of .</p>

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33

FERRAGUTI, ANDREA, and GIACOMO MICHELI. "ON THE MERTENS–CESÀRO THEOREM FOR NUMBER FIELDS." Bulletin of the Australian Mathematical Society 93, no. 2 (November 11, 2015): 199–210. http://dx.doi.org/10.1017/s0004972715001288.

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Let $K$ be a number field with ring of integers ${\mathcal{O}}$. After introducing a suitable notion of density for subsets of ${\mathcal{O}}$, generalising the natural density for subsets of $\mathbb{Z}$, we show that the density of the set of coprime $m$-tuples of algebraic integers is $1/{\it\zeta}_{K}(m)$, where ${\it\zeta}_{K}$ is the Dedekind zeta function of $K$. This generalises a result found independently by Mertens [‘Ueber einige asymptotische Gesetze der Zahlentheorie’, J. reine angew. Math. 77 (1874), 289–338] and Cesàro [‘Question 75 (solution)’, Mathesis 3 (1883), 224–225] concerning the density of coprime pairs of integers in $\mathbb{Z}$.

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34

KATAYAMA, Koji. "Barnes' Double Zeta Function, the Dedekind Sum and Ramanujan's Formula." Tokyo Journal of Mathematics 27, no. 1 (June 2004): 41–56. http://dx.doi.org/10.3836/tjm/1244208473.

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35

Hashimoto, Yasufumi, Yasuyuki Iijima, Nobushige Kurokawa, and Masato Wakayama. "Euler's constants for the Selberg and the Dedekind zeta functions." Bulletin of the Belgian Mathematical Society - Simon Stevin 11, no. 4 (December 2004): 493–516. http://dx.doi.org/10.36045/bbms/1102689119.

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36

Sono, Keiju. "Continuous lower bounds for the moments of Dedekind zeta-functions." Journal of Number Theory 188 (July 2018): 335–56. http://dx.doi.org/10.1016/j.jnt.2018.01.014.

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37

Omar, Sami. "Localization of the first zero of the Dedekind zeta function." Mathematics of Computation 70, no. 236 (March 7, 2001): 1607–17. http://dx.doi.org/10.1090/s0025-5718-01-01305-9.

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38

Chua, Kok Seng. "Real zeros of Dedekind zeta functions of real quadratic fields." Mathematics of Computation 74, no. 251 (July 21, 2004): 1457–71. http://dx.doi.org/10.1090/s0025-5718-04-01701-6.

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39

Kim, Hyun Kwang, and Hyung Ju Hwang. "Values of zeta functions and class number 1 criterion for the simplest cubic fields." Nagoya Mathematical Journal 160 (2000): 161–80. http://dx.doi.org/10.1017/s0027763000007741.

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AbstractLet K be the simplest cubic field defined by the irreducible polynomial where m is a nonnegative rational integer such that m2 + 3m + 9 is square-free. We estimate the value of the Dedekind zeta function ζK(s) at s = −1 and get class number 1 criterion for the simplest cubic fields.

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40

Louboutin, Stéphane. "Class-number problems for cubic number fields." Nagoya Mathematical Journal 138 (June 1995): 199–208. http://dx.doi.org/10.1017/s0027763000005249.

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Let M be any number field. We let DM, dM, hu, , AM and RegM be the discriminant, the absolute value of the discriminant, the class-number, the Dedekind zeta-function, the ring of algebraic integers and the regulator of M, respectively.we set If q is any odd prime we let (⋅/q) denote the Legendre’s symbol.

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41

Boyd, David W., and Fernando Rodriguez-Villegas. "Mahler’s Measure and the Dilogarithm (I)." Canadian Journal of Mathematics 54, no. 3 (June 1, 2002): 468–92. http://dx.doi.org/10.4153/cjm-2002-016-9.

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AbstractAn explicit formula is derived for the logarithmicMahler measurem(P) of P(x, y) = p(x)y− q(x), where p(x) and q(x) are cyclotomic. This is used to find many examples of such polynomials for which m(P) is rationally related to the Dedekind zeta value ζF(2) for certain quadratic and quartic fields.

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42

Browkin, Jerzy, and Herbert Gangl. "Tame kernels and second regulators of number fields and their subfields." Journal of K-Theory 12, no. 1 (July 17, 2013): 137–65. http://dx.doi.org/10.1017/is013005031jkt229.

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AbstractAssuming a version of the Lichtenbaum conjecture, we apply Brauer-Kuroda relations between the Dedekind zeta function of a number field and the zeta function of some of its subfields to prove formulas relating the order of the tame kernel of a number field F with the orders of the tame kernels of some of its subfields. The details are given for fields F which are Galois over ℚ with Galois group the group ℤ/2 × ℤ/2, the dihedral group D2p; p an odd prime, or the alternating group A4. We include numerical results illustrating these formulas.

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43

Harper, Malcolm, and M. Ram Murty. "Euclidean Rings of Algebraic Integers." Canadian Journal of Mathematics 56, no. 1 (February 1, 2004): 71–76. http://dx.doi.org/10.4153/cjm-2004-004-5.

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AbstractLet K be a finite Galois extension of the field of rational numbers with unit rank greater than 3. We prove that the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain. This was previously known under the assumption of the generalized Riemann hypothesis for Dedekind zeta functions. We now prove this unconditionally.

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44

Zykin, Alexey. "Asymptotic properties of Dedekind zeta functions in families of number fields." Journal de Théorie des Nombres de Bordeaux 22, no. 3 (2010): 771–78. http://dx.doi.org/10.5802/jtnb.746.

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45

Paul, Biplab, and Ayyadurai Sankaranarayanan. "On the error term and zeros of the Dedekind zeta function." Journal of Number Theory 215 (October 2020): 98–119. http://dx.doi.org/10.1016/j.jnt.2020.02.006.

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46

Foote, Richard, and David Wales. "Zeros of order 2 of Dedekind zeta functions and Artin's Conjecture." Journal of Algebra 131, no. 1 (May 1990): 226–57. http://dx.doi.org/10.1016/0021-8693(90)90173-l.

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47

Turnage-Butterbaugh, Caroline L. "Gaps between zeros of Dedekind zeta-functions of quadratic number fields." Journal of Mathematical Analysis and Applications 418, no. 1 (October 2014): 100–107. http://dx.doi.org/10.1016/j.jmaa.2014.03.074.

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48

Banerjee, Soumyarup, Kalyan Chakraborty, and Azizul Hoque. "An analogue of Wilton's formula and values of Dedekind zeta functions." Journal of Mathematical Analysis and Applications 495, no. 1 (March 2021): 124675. http://dx.doi.org/10.1016/j.jmaa.2020.124675.

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49

Lee, Ethan S. "On an explicit zero-free region for the Dedekind zeta-function." Journal of Number Theory 224 (July 2021): 307–22. http://dx.doi.org/10.1016/j.jnt.2020.12.015.

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50

Müller, Wolfgang. "The mean square of the Dedekind zeta function in quadratic number fields." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 3 (November 1989): 403–17. http://dx.doi.org/10.1017/s0305004100068134.

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Let K be a quadratic number field with discriminant D. The aim of this paper is to study the mean square of the Dedekind zeta function ζK on the critical line, i.e.It was proved by Chandrasekharan and Narasimhan[1] that (1) is at most of order O(T(log T)2). As they noted at the end of their paper, it ‘would seem likely’ that (1) behaves asymptotically like a2T(log T)2, with some constant a2 depending on K. Applying a general mean value theorem for Dirichlet polynomials, one can actually proveThis may be done in just the same way as this general mean value theorem can be used to prove Ingham's classical result on the fourth power moment of the Riemann zeta function (cf. [3], chapter 5). In 1979 Heath-Brown [2] improved substantially on Ingham's result. Adapting his method to the above situation a much better result than (2) can be obtained. The following Theorem deals with a slightly more general situation. Note that ζK(s) = ζ(s)L(s, XD) where XD is a real primitive Dirichlet character modulo |D|. There is no additional difficulty in allowing x to be complex.

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