A new solution to the equation .
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Lygeros, Nik, Rozier, Olivier (2010)
Journal of Integer Sequences [electronic only]
Habiba Kadiri (2013)
Acta Arithmetica
We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
Booker, Andrew R. (2006)
Experimental Mathematics
José Luis Gómez Pardo (2001)
Gaceta de la Real Sociedad Matemática Española
Anne-Maria Ernvall-Hytönen, Arto Lepistö (2009)
Acta Mathematica Universitatis Ostraviensis
The aim of this paper is to present some computer data suggesting the correct size of bounds for exponential sums of Fourier coefficients of holomorphic cusp forms.
Rubinstein, Michael, Sarnak, Peter (1994)
Experimental Mathematics
Ben Kane (2009)
Journal de Théorie des Nombres de Bordeaux
Assuming GRH, we present an algorithm which inputs a prime and outputs the set of fundamental discriminants such that the reduction map modulo a prime above from elliptic curves with CM by to supersingular elliptic curves in characteristic is surjective. In the algorithm we first determine an explicit constant so that implies that the map is necessarily surjective and then we compute explicitly the cases .
Peng Tian (2014)
Acta Arithmetica
We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct. As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved uper bound on...
John Voight (2009)
Journal de Théorie des Nombres de Bordeaux
We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group with cofinite area. As a consequence, we compute the invariants of , including an explicit finite presentation for .
Watkins, Mark (2002)
Experimental Mathematics
Deléglise, Marc, Rivat, Joël (1996)
Experimental Mathematics
Cohen, Henri, Rodriguez Villegas, Fernando, Zagier, Don (2000)
Experimental Mathematics
Caldwell, Chris K., Cheng, Yuanyou (2005)
Journal of Integer Sequences [electronic only]
Olivier Ramaré (2014)
Acta Arithmetica
We prove that for every x > q ≥ 1, and similar estimates for the Liouville function. We also give better constants when x/q is large.,
David J. Platt, Sumaia Saad Eddin (2013)
Colloquium Mathematicae
Let χ be a primitive Dirichlet character of conductor q and denote by L(z,χ) the associated L-series. We provide an explicit upper bound for |L(1,χ)| when 3 divides q.
Amdeberhan, Tewodros (1996)
The Electronic Journal of Combinatorics [electronic only]
M. El Marraki (1995)
Journal de théorie des nombres de Bordeaux
On établit les majorations , valable pour qui est la meilleure majoration possible en valable pour tout , et d’autres analogues. On montre enfin comment trouver des majorations effectives pour tout .
Olivier Ramaré (2013)
Acta Arithmetica
Baier, Harald, Köhler, Günter (2003)
Experimental Mathematics
Crandall, Richard E. (1999)
Experimental Mathematics
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