3,847 research outputs found
An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials
In 1997 the author 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
obtained an arithmetic formula for these coefficients using the ``explicit
formula'' of prime number theory. In this paper, the author obtains an
arithmetic formula for corresponding coefficients associated with the Euler
product of Hecke polynomials, which is essentially a product of L-functions
attached to weight 2 cusp forms (both newforms and oldforms) over Hecke
congruence subgroups. The nonnegativity of these coefficients gives a criterion
for the Riemann hypothesis for all these L-functions at once
A new problem in string searching
We describe a substring search problem that arises in group presentation
simplification processes. We suggest a two-level searching model: skip and
match levels. We give two timestamp algorithms which skip searching parts of
the text where there are no matches at all and prove their correctness. At the
match level, we consider Harrison signature, Karp-Rabin fingerprint, Bloom
filter and automata based matching algorithms and present experimental
performance figures.Comment: To appear in Proceedings Fifth Annual International Symposium on
Algorithms and Computation (ISAAC'94), Lecture Notes in Computer Scienc
Causality of black holes in 4-dimensional Einstein-Gauss-Bonnet-Maxwell theory
We study charged black hole solutions in 4-dimensional (4D)
Einstein-Gauss-Bonnet-Maxwell theory to the linearized perturbation level. We
first compute the shear viscosity to entropy density ratio. We then demonstrate
how bulk causal structure analysis imposes a upper bound on the Gauss-Bonnet
coupling constant in the AdS space. Causality constrains the value of
Gauss-Bonnet coupling constant to be bounded by as .Comment: 13 pages, minor revision, references adde
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