Rationality of Partial Zeta Functions

@article{Wan2003RationalityOP,
  title={Rationality of Partial Zeta Functions},
  author={Daqing Wan},
  journal={Indagationes Mathematicae},
  year={2003},
  volume={14},
  pages={285-292}
}
  • D. Wan
  • Published 10 April 2003
  • Mathematics
  • Indagationes Mathematicae
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6 Citations
Highly Influential Citations
1
Background Citations
2
Methods Citations
1

6 Citations

Citation Type

Citation Type

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References

SHOWING 1-10 OF 11 REFERENCES
TOTAL DEGREE BOUNDS FOR ARTIN L-FUNCTIONS AND PARTIAL ZETA FUNCTIONS
Let Fq be a finite field of characteristic p with q elements. Choose an algebraic closure F of Fq. Throughout this paper, schemes, morphisms and sheaves defined over the base field Fq are denoted by…
Partial Zeta Functions of Algebraic Varieties over Finite Fields
Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety defined over a finite field. We then…
On the Rationality of the Zeta Function of an Algebraic Variety
Let p be a prime number, a2 the completion of the algebraic closure of the field of rational p-adic numbers and let A be the residue class field of Q. The field A is the algebraic closure of its…
Sums of Betti Numbers in Arbitrary Characteristic
La conjecture de Weil. I
© Publications mathematiques de l’I.H.E.S., 1974, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.…
Rank one case of Dwork's conjecture
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Xxxx XXXX, Pages 000–000 S 0894-0347(XX)0000-0 arXiv:math/0005308v1 [math.NT] 9 May 2000 RANK ONE CASE OF DWORK’S CONJECTURE DAQING…
Frobenius–Schur Indicator and the Ubiquity of Brock–Granville Quadratic Excess
Introduction In a recent paper, Brock and Granville consider the following question. Fix a genus g ≥ 1. For a finite field Éq of odd characteristic, denote by S2g+1(Éq) the set of those monic…
Moment L-functions, partial L-functions and partial exponential sums
Higher rank case of Dwork's conjecture
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 00, Number 0, Xxxx XXXX, Pages 000–000 S 0894-0347(XX)0000-0 arXiv:math/0005309v1 [math.NT] 9 May 2000 HIGHER RANK CASE OF DWORK’S CONJECTURE…
Geometric moment zeta functions
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