Edizione	[Reprint 2011]
Pubbl/distr/stampa	Berlin ; ; New York, : W. de Gruyter, 1991
Descrizione fisica	1 online resource (356 p.)
Disciplina	512/.7
Altri autori (Persone)	PethöAttila <1950->
Soggetto topico	Number theory - Data processing
Soggetto genere / forma	Electronic books.
ISBN	3-11-086595-5
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	Front matter -- Preface -- List of contributors -- Table of contents -- On the construction of primitive elements and primitive normal bases in a finite field / Stepanov, S.A. / Shparlinskiy, I.E. -- A numerical method for the determination of the cyclotomic polynomial coefficients / Grytczuk, A. / Tropak, B. -- Number systems / Kovács, Β. -- Fast converging series representations of real numbers and their implementations in digital processing / Melnichuk, Yu. V. -- On a polynomial transformation and its application to the construction of a public key cryptosystem / Pethö, A. -- Number-theoretic transforms and a theorem of Sylvester - Kronecker - Zsigmondy / Tasche, M. / Steidl, G. / Creutzburg, R. -- A probabilistic class group and regulator algorithm and its implementation / Buchmann, J. / Düllmann, S. -- Prime-producing quadratic polynomials and class numbers of quadratic orders / Halter-Koch, F. -- Applications of a new class number two criterion for real quadratic fields / Mollin, R.A. -- On a solution of a class number two problem for a family of real quadratic fields / Mollin, R.A. / Williams, H.C. -- Cubic number fields with exceptional units / Ennola, V. -- Enumeration of totally complex quartic fields of small discriminant / Ford, D. -- Class number computation by cyclotomic or elliptic units / Nakamula, K. -- Computing fundamental units from independent units / Arenz, B. -- A note on index divisors / Pohst, M. -- Computation of independent units in number fields by a combination of the methods of Buchmann/Pethö and Pohst / Zassenhaus / Schröter, U. -- Hecke actions on classes of ternary quadratic forms / Birch, B.J. -- Computation of singular moduli by multi-valued modular equations / Cohn, Harvey -- Congruent numbers and elliptic curves / Serf, P. -- The rank of elliptic curves upon quadratic extension / Schneiders, U. / Zimmer, H. G. -- On the resolution of some diophantine equations / Gaál, I. -- Index form equations in cubic number fields / Schulte, Ν. -- On the practical solution of the Thue-Mahler equation / Tzanakis, N. / Weger, B.M.M. de -- Some results on Thue equations and Thue-Mahler equations / Evertse, J.H. / -- On the solution of the diophantine equation Gn = P(x) with sieve algorithm / Nemes, I. -- On Thue equations associated with certain quartic number fields / Stroeker, R.J. -- KANT - a tool for computations in algebraic number fields / Graf, J. / -- SIMATH - a computer algebra system / Hollinger, C. / Serf, P.
Record Nr.	UNINA-9910462532603321

Autore	Hejhal Dennis A.
Pubbl/distr/stampa	Providence, Rhode Island, United States : , : American Mathematical Society, , 1992
Descrizione fisica	1 online resource (177 p.)
Disciplina	512/.7
Collana	Memoirs of the American Mathematical Society
Soggetto topico	Selberg trace formula Automorphic functions Eigenvalues Laplacian operator
Soggetto genere / forma	Electronic books.
ISBN	1-4704-0895-3
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	""Table of Contents""; ""0. Foreword""; ""I. Eigenvalues of the Laplacian for Hecke Triangle Groups""; ""1. Introduction and preliminary remarks""; ""2. The procedure in a nutshell""; ""3. Some theoretical difficulties""; ""4. Coefficient relations for N = 4 and 6""; ""5. ""Odd"" eigenvalues for N = 4, 5, 6, 7""; ""6. ""Even"" eigenvalues for N = 4, 5, 6, 7""; ""7. Some examples""; ""8. Some remarks about pseudo cusp forms""; ""9. Concluding remarks""; ""References""; ""Appendix A""; ""II. (Reprint of) Eigenvalues of the Laplacian for PSL(2,Z): Some New Results and Computational Techniques"" ""1. Introduction""""2. The basic procedure""; ""3. Some informal remarks concerning implementation of the basic procedure""; ""4. Further remarks""; ""5. The even eigenvalues less than 50""; ""6. The odd eigenvalues less than 50""; ""7. Even eigenvalues around R = 125""; ""8. Even eigenvalues around R = 250""; ""9. Even eigenvalues around R = 500""; ""10. Gaining greater accuracy""; ""11. Concluding remarks""; ""References""; ""Appendix B""
Record Nr.	UNINA-9910480745103321

Autore	Jones Gareth A
Edizione	[1st ed. 1998.]
Pubbl/distr/stampa	London : , : Springer London : , : Imprint : Springer, , 1998
Descrizione fisica	1 online resource (XIV, 302 p.)
Disciplina	512/.7
Collana	Springer Undergraduate Mathematics Series
Soggetto topico	Number theory Number Theory
ISBN	1-4471-0613-X
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Nota di contenuto	1. Divisibility -- 1.1 Divisors -- 1.2 Bezout’s identity -- 1.3 Least common multiples -- 1.4 Linear Diophantine equations -- 1.5 Supplementary exercises -- 2. Prime Numbers -- 2.1 Prime numbers and prime-power factorisations -- 2.2 Distribution of primes -- 2.3 Fermat and Mersenne primes -- 2.4 Primality-testing and factorisation -- 2.5 Supplementary exercises -- 3. Congruences -- 3.1 Modular arithmetic -- 3.2 Linear congruences -- 3.3 Simultaneous linear congruences -- 3.4 Simultaneous non-linear congruences -- 3.5 An extension of the Chinese Remainder Theorem -- 3.6 Supplementary exercises -- 4. Congruences with a Prime-power Modulus -- 4.1 The arithmetic of ?p -- 4.2 Pseudoprimes and Carmichael numbers -- 4.3 Solving congruences mod (pe) -- 4.4 Supplementary exercises -- 5. Euler’s Function -- 5.1 Units -- 5.2 Euler’s function -- 5.3 Applications of Euler’s function -- 5.4 Supplementary exercises -- 6. The Group of Units -- 6.1 The group Un -- 6.2 Primitive roots -- 6.3 The group Une, where p is an odd prime -- 6.4 The group U2e -- 6.5 The existence of primitive roots -- 6.6 Applications of primitive roots -- 6.7 The algebraic structure of Un -- 6.8 The universal exponent -- 6.9 Supplementary exercises -- 7. Quadratic Residues -- 7.1 Quadratic congruences -- 7.2 The group of quadratic residues -- 7.3 The Legendre symbol -- 7.4 Quadratic reciprocity -- 7.5 Quadratic residues for prime-power moduli -- 7.6 Quadratic residues for arbitrary moduli -- 7.7 Supplementary exercises -- 8. Arithmetic Functions -- 8.1 Definition and examples -- 8.2 Perfect numbers -- 8.3 The Mobius Inversion Formula -- 8.4 An application of the Mobius Inversion Formula -- 8.5 Properties of the Mobius function -- 8.6 The Dirichlet product -- 8.7 Supplementary exercises -- 9. The Riemann Zeta Function -- 9.1 Historical background -- 9.2 Convergence -- 9.3 Applications to prime numbers -- 9.4 Random integers -- 9.5 Evaluating ?(2) -- 9.6 Evaluating ?(2k) -- 9.7 Dirichlet series -- 9.8 Euler products -- 9.9 Complex variables -- 9.10 Supplementary exercises -- 10. Sums of Squares -- 10.1 Sums of two squares -- 10.2 The Gaussian integers -- 10.3 Sums of three squares -- 10.4 Sums of four squares -- 10.5 Digression on quaternions -- 10.6 Minkowski’s Theorem -- 10.7 Supplementary exercises -- 11. Fermat’s Last Theorem -- 11.1 The problem -- 11.2 Pythagoras’s Theorem -- 11.3 Pythagorean triples -- 11.4 Isosceles triangles and irrationality -- 11.5 The classification of Pythagorean triples -- 11.6 Fermat -- 11.7 The case n = 4 -- 11.8 Odd prime exponents -- 11.9 Lame and Kummer -- 11.10 Modern developments -- 11.11 Further reading -- Solutions to Exercises -- Index of symbols -- Index of names.
Record Nr.	UNINA-9910479869403321

Autore	Jorgenson Jay
Edizione	[1st ed. 1994.]
Pubbl/distr/stampa	Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1994]
Descrizione fisica	1 online resource (VIII, 160 p.)
Disciplina	512/.7
Collana	Lecture Notes in Mathematics
Soggetto topico	Spectral theory (Mathematics) Sequences (Mathematics) Number theory Functions, Zeta
ISBN	3-540-49041-8
Classificazione	11M36
Formato	Materiale a stampa
Livello bibliografico	Monografia
Lingua di pubblicazione	eng
Record Nr.	UNISA-996466373503316