Compact groups and dirichlet series
نویسندگان
چکیده
منابع مشابه
Lacunary Fourier Series for Compact Quantum Groups
This paper is devoted to the study of Sidon sets, Λ(p)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, Λ(p)-sets and lacunarities for LFourier multipliers, generali...
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This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...
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where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...
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1. J. W. S. Cassels, An introduction to diophantine approximation, Cambridge University Press, 1959, Chapter IV, §5. 2. J. F. Koksma, Diophantische Approximationen, Ergebnisse der Mathematik, vol. IV, Berlin, Springer, 1937, Chapter VIII, §3. 3. G. M. Petersen, Almost convergence and uniformly distributed sequences, Quart. J. Math. vol. 7 (1956) pp. 188-191. 4. H. Weyl, Uber die Gleichverteilun...
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For a fixed hyperelliptic curve C given by the equation y 1⁄4 f ðxÞ with f A Z1⁄2x having distinct roots and degree at least 5, we study the variation of rational points on the quadratic twists Cm whose equation is given by my 2 1⁄4 f ðxÞ. More precisely, we study the Dirichlet series Df ðsÞ 1⁄4 P 0 m00aCmðQÞjmj s where the summation is over all non-zero squarefree integers. We show that Df ðsÞ...
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1970
ISSN: 0004-2080
DOI: 10.1007/bf02589554