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291,709
THE EXPLICIT FORMULA IN SIMPLE TERMS
, 1998
"... This is a semiexpository paper on the easier aspects of the Explicit Formula for the Riemann Zeta Function. The topics reviewed here include: Weil’s criterion for the Riemann Hypothesis and its probabilistic interpretation, various formulations of the contribution corresponding to the real place, H ..."
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Cited by 2 (1 self)
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This is a semiexpository paper on the easier aspects of the Explicit Formula for the Riemann Zeta Function. The topics reviewed here include: Weil’s criterion for the Riemann Hypothesis and its probabilistic interpretation, various formulations of the contribution corresponding to the real place
An explicit formula for Siegel series
 Amer. J. Math
, 1999
"... Abstract. Combining induction formulas for local densities with a functional equation for the Siegel series, we give an explicit formula for the Siegel series. By this formula, we also give an explicit formula for the Fourier coefficients of the Siegel Eisenstein series. Introduction. The Siegel Eis ..."
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Cited by 27 (7 self)
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Abstract. Combining induction formulas for local densities with a functional equation for the Siegel series, we give an explicit formula for the Siegel series. By this formula, we also give an explicit formula for the Fourier coefficients of the Siegel Eisenstein series. Introduction. The Siegel
An Explicit Formula for the Spherical Curves
"... The purpose of this article is to give an explicit formula for all curves of constant torsion τ in the unit twosphere S2(1). These curves and their basic properties have been known since the 1890’s, and some of these properties are discussed in the Appendix. Some example curves, computed with a sta ..."
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The purpose of this article is to give an explicit formula for all curves of constant torsion τ in the unit twosphere S2(1). These curves and their basic properties have been known since the 1890’s, and some of these properties are discussed in the Appendix. Some example curves, computed with a
EXPLICIT FORMULAS FOR 2CHARACTERS
, 904
"... Abstract. Ganter and Kapranov associated a 2character to 2representations of a finite group. Elgueta classified 2representations in the category of 2vector spaces 2V ectk in terms of cohomological data. We give an explicit formula for the 2character in terms of this cohomological data and deriv ..."
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Cited by 1 (0 self)
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Abstract. Ganter and Kapranov associated a 2character to 2representations of a finite group. Elgueta classified 2representations in the category of 2vector spaces 2V ectk in terms of cohomological data. We give an explicit formula for the 2character in terms of this cohomological data
The Explicit Formula and the conductor operator
, 1999
"... I give a new derivation of the Explicit Formula for an arbitrary number field and abelian DirichletHecke character, which treats all primes in exactly the same way, whether they are discrete or archimedean, and also ramified or not. This is followed with a local study of a Hilbert space operator, t ..."
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Cited by 5 (3 self)
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I give a new derivation of the Explicit Formula for an arbitrary number field and abelian DirichletHecke character, which treats all primes in exactly the same way, whether they are discrete or archimedean, and also ramified or not. This is followed with a local study of a Hilbert space operator
Explicit Formulas for Some Generalized Polynomials
, 2013
"... Abstract: Using notions of composita and composition of generating functions, we establish some explicit formulas for the ..."
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Abstract: Using notions of composita and composition of generating functions, we establish some explicit formulas for the
EXPLICIT FORMULAS FOR NUMBERS OF RAMANUJAN
, 1984
"... In Chapter 3 of his second notebook [1, p. 165]9 Ramanujan defined numbers a (ft, k) such that a(2, 0) = 1 and for n ^ 2, a(n + 1, k) = (ft l)a(ft, fc 1) + (2n 1 k)a(n9 k). (1.1) He defined a (ft, &) = 0 when fc<0or/c>ft2. The numbers were used in the ..."
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Cited by 2 (1 self)
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In Chapter 3 of his second notebook [1, p. 165]9 Ramanujan defined numbers a (ft, k) such that a(2, 0) = 1 and for n ^ 2, a(n + 1, k) = (ft l)a(ft, fc 1) + (2n 1 k)a(n9 k). (1.1) He defined a (ft, &) = 0 when fc<0or/c>ft2. The numbers were used in the
Explicit formulas for the Hilbert symbol
 GEOMETRY & TOPOLOGY MONOGRAPHS VOLUME 3: INVITATION TO HIGHER LOCAL FIELDS PART I, SECTION 8, PAGES 81–89
, 2000
"... Recall that the Hilbert symbol for a local field K with finite residue field which contains a primitive pn th root of unity ζpn is a pairing ( ,)p n:K ∗ /K ∗pn × K ∗ ∗ pn /K → 〈ζpn〉, (α,β)p n = γΨK(α)−1 p, γ n = β, where ΨK:K ∗ → Gal(K ab /K) is the reciprocity map. ..."
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Recall that the Hilbert symbol for a local field K with finite residue field which contains a primitive pn th root of unity ζpn is a pairing ( ,)p n:K ∗ /K ∗pn × K ∗ ∗ pn /K → 〈ζpn〉, (α,β)p n = γΨK(α)−1 p, γ n = β, where ΨK:K ∗ → Gal(K ab /K) is the reciprocity map.
Exponential maps and explicit formulas
 GEOMETRY & TOPOLOGY MONOGRAPHS VOLUME 3: INVITATION TO HIGHER LOCAL FIELDS PART I, SECTION 9, PAGES 91–94
, 2000
"... ..."
EXPLICIT FORMULAS FOR THE MULTIVARIATE RESULTANT
, 2000
"... Abstract. We present formulas for the multivariate resultant as a quotient of two determinants. They extend the classical Macaulay formulas, and involve matrices of considerably smaller size, whose non zero entries include coefficients of the given polynomials and coefficients of their Bezoutian. Th ..."
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Cited by 3 (0 self)
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. These formulas can also be viewed as an explicit computation of the morphisms and the determinant of a resultant complex. 1.
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