Preprints (rote Reihe) des Fachbereich Mathematik
Refine
Keywords
- Dirichlet series (1)
- Riemann-Siegel formula (1)
- Translation planes (1)
- Verschlüsselung (1)
- Vigenere (1)
- cusp forms (1)
- ovoids (1)
- quadratic forms (1)
Faculty / Organisational entity
312
Vigenere-Verschlüsselung
(1999)
300
286
An analogue of the classical Riemann-Siegel integral formula for Dirichlet series associated to cusp forms is developed. As an application of the formula, we give a comparatively simple proof of the approximate functional equation for this type of Dirichlet series.
216
We present a generalization of Proth's theorem for testing certain large integers for primality. The use of Gauß sums leads to a much simpler approach to these primality criteria as compared to the earlier tests. The running time of the algorithms is bounded by a polynomial in the length of the input string. The applicability of our algorithms is linked to certain diophantine approximations of \(l\)-adic roots of unity.
219
A Remark on Primes of the Form \(2^{3n}a + 2^{2n}b+2^nc+1\). Necessary and sufficient conditions for the numbers in the title to be prime are given. The tests are well suited for practical purposes.
218