Dirichlet series associated with polynomials

Manfred Peter

Acta Arithmetica (1998)

  • Volume: 84, Issue: 3, page 245-278
  • ISSN: 0065-1036

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Manfred Peter. "Dirichlet series associated with polynomials." Acta Arithmetica 84.3 (1998): 245-278. <http://eudml.org/doc/207145>.

@article{ManfredPeter1998,
author = {Manfred Peter},
journal = {Acta Arithmetica},
keywords = {Dirichlet series; analytic continuation; singularities; asymptotic formula for the summatory function},
language = {eng},
number = {3},
pages = {245-278},
title = {Dirichlet series associated with polynomials},
url = {http://eudml.org/doc/207145},
volume = {84},
year = {1998},
}

TY - JOUR
AU - Manfred Peter
TI - Dirichlet series associated with polynomials
JO - Acta Arithmetica
PY - 1998
VL - 84
IS - 3
SP - 245
EP - 278
LA - eng
KW - Dirichlet series; analytic continuation; singularities; asymptotic formula for the summatory function
UR - http://eudml.org/doc/207145
ER -

References

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  1. [1] P. Cassou-Noguès, Valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme I, J. Number Theory 14 (1982), 32-64. Zbl0496.12008
  2. [2] H. Davenport, Multiplicative Number Theory, Markham, 1967. 
  3. [3] J. Jorgenson and S. Lang, Basic Analysis of Regularized Series and Products, Lecture Notes in Math. 1564, Springer, 1993. Zbl0788.30003
  4. [4] B. Lichtin, Generalized Dirichlet series and b-functions, Compositio Math. 65 (1988), 81-120. 
  5. [5] B. Lichtin, The asymptotics of a lattice point problem associated to a finite number of polynomials I, II, Duke Math. J. 63 (1991), 139-192; 77 (1995), 699-751. Zbl0735.11048
  6. [6] K. Mahler, Über einen Satz von Mellin, Math. Ann. 100 (1928), 384-395. 
  7. [7] Hj. Mellin, Eine Formel für den Logarithmus transcendenter Functionen von endlichem Geschlecht, Acta Soc. Sci. Fenn. 29 (1900), no. 4. 
  8. [8] Hj. Mellin, Die Dirichlet'schen Reihen, die zahlentheoretischen Funktionen und die unendlichen Produkte von endlichem Geschlecht, Acta Math. 28 (1904), 37-64. 
  9. [9] P. Sargos, Prolongement méromorphe des séries de Dirichlet associées à des fractions rationnelles de plusieurs variables, Ann. Inst. Fourier (Grenoble) 34 (3) (1984), 83-123. Zbl0523.10026
  10. [10] P. Sargos, Croissance de certaines séries de Dirichlet et applications, J. Reine Angew. Math. 367 (1986), 139-154. Zbl0575.10035
  11. [11] G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Publ. Inst. Elie Cartan, Université de Nancy, 1990. 

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