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On the Satisfiability of Modular Arithmetic Formulae
"... Abstract. Modular arithmetic is the underlying integral computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of propositional formulae in modular arithmetic can be obtained by solving alternationfree Presburger arithmetic, it is easy to see t ..."
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Abstract. Modular arithmetic is the underlying integral computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of propositional formulae in modular arithmetic can be obtained by solving alternationfree Presburger arithmetic, it is easy to see
TensorRank and Lower Bounds for Arithmetic Formulas
"... We show that any explicit example for a tensor A: [n] r → F with tensorrank ≥ nr·(1−o(1)) , (where r = r(n) ≤ log n / log log n), implies an explicit superpolynomial lower bound for the size of general arithmetic formulas over F. This shows that strong enough lower bounds for the size of arithmet ..."
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Cited by 20 (1 self)
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We show that any explicit example for a tensor A: [n] r → F with tensorrank ≥ nr·(1−o(1)) , (where r = r(n) ≤ log n / log log n), implies an explicit superpolynomial lower bound for the size of general arithmetic formulas over F. This shows that strong enough lower bounds for the size
On Arithmetical Formulas Whose Jacobians are Gröbner Bases
, 2000
"... We exhibit classes of polynomials whose sets of kth partial derivatives form Gröbner bases for all k, with respect to all term orders. The classes are defined by syntactic constraints on arithmetical formulas defining the polynomials. Readonce formulas without constants have this property for al ..."
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We exhibit classes of polynomials whose sets of kth partial derivatives form Gröbner bases for all k, with respect to all term orders. The classes are defined by syntactic constraints on arithmetical formulas defining the polynomials. Readonce formulas without constants have this property
On Arithmetical Formulas Whose Jacobians are Gröbner Bases
, 2000
"... We exhibit classes of polynomials whose sets of kth partial derivatives form Gröbner bases for all k, with respect to all term orders. The classes are defined by syntactic constraints on arithmetical formulas defining the polynomials. Readonce formulas without constants have this property for all k ..."
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We exhibit classes of polynomials whose sets of kth partial derivatives form Gröbner bases for all k, with respect to all term orders. The classes are defined by syntactic constraints on arithmetical formulas defining the polynomials. Readonce formulas without constants have this property for all
Depth3 arithmetic formulae over fields of characteristic zero
 In CCC
, 1999
"... In this paper we prove near quadratic lower bounds for depth3 arithmetic formulae over fields of characteristic zero. Such bounds are obtained for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant. As corollaries we get the first nontrivial lower ..."
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Cited by 18 (2 self)
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In this paper we prove near quadratic lower bounds for depth3 arithmetic formulae over fields of characteristic zero. Such bounds are obtained for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant. As corollaries we get the first nontrivial
AN ARITHMETIC FORMULA FOR CERTAIN COEFFICIENTS OF THE EULER PRODUCT OF HECKE POLYNOMIALS
, 2004
"... Abstract. In 1997 the author [11] found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias [2] obtained an arithmetic formula for these coefficients using t ..."
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Abstract. In 1997 the author [11] found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias [2] obtained an arithmetic formula for these coefficients using
A superpolynomial lower bound for regular arithmetic formulas.
 In Proc. 46th Annual ACM Symposium on the Theory of Computing,
, 2014
"... Abstract We consider arithmetic formulas consisting of alternating layers of addition (+) and multiplication (×) gates such that the fanin of all the gates in any fixed layer is the same. Such a formula Φ which additionally has the property that its formal/syntactic degree is at most twice the (tot ..."
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Cited by 15 (6 self)
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Abstract We consider arithmetic formulas consisting of alternating layers of addition (+) and multiplication (×) gates such that the fanin of all the gates in any fixed layer is the same. Such a formula Φ which additionally has the property that its formal/syntactic degree is at most twice
A derivation of the Hardy–Ramanujan formula from an arithmetic formula
, 2012
"... We reprove the HardyRamanujan asymptotic formula for the partition function without using the circle method. We derive our result from recent work of Bruinier and Ono on harmonic weak Maass forms. ..."
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Cited by 2 (2 self)
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We reprove the HardyRamanujan asymptotic formula for the partition function without using the circle method. We derive our result from recent work of Bruinier and Ono on harmonic weak Maass forms.
Results 1  10
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1,317