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2012, Annals of mathematics studies, ISBN 0691153310, Volume 180, vi, 203
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin... 
Sequences (Mathematics) | Convolutions (Mathematics) | Mellin transform | Mathematics | Statistics
Book
Classical and Quantum Gravity, ISSN 0264-9381, 10/2010, Volume 27, Issue 20, p. 205006
Within 5-10 years, very long baseline interferometry facilities will be able to observe the 'shadow' of super-massive black hole candidates. This will allow... 
MULTIPOLE MOMENTS | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | MASS | GALACTIC-CENTER | EVENT-HORIZON | KERR | BLACK-HOLE | PHYSICS, PARTICLES & FIELDS
Journal Article
Inventiones Mathematicae, ISSN 0020-9910, 2016, Volume 203, Issue 1, pp. 1 - 177
We consider certain families of automorphic representations over number fields arising from the principle of functoriality of Langlands. Let be a reductive... 
P-ADIC GROUPS | MATHEMATICS | MOTIVIC INTEGRATION | LIE-GROUPS | STABLE TRACE FORMULA | EULER PRODUCTS | RANDOM-MATRIX THEORY | HECKE OPERATORS | REDUCTIVE GROUPS | POWER L-FUNCTIONS | MODULAR-FORMS | Theorems | Infinity | Eigenvalues | Isomorphism | Fuel consumption | Representations | Symmetry
Journal Article
Economics Letters, ISSN 0165-1765, 10/2019, Volume 183, p. 108535
The Sato–Vartia (SV) index for bilateral price comparisons has impressive analytical properties and is used intensively in recent international trade and... 
Sato–Vartia index | Transitivity | Factor reversal test | Multilateral comparisons | ECONOMICS | Sato-Vartia index | Prices | International trade | Macroeconomics | Indexes | Number theory
Journal Article
Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 2019, Volume 100, Issue 1, pp. 27 - 33
We establish an error term in the Sato-Tate theorem of Birch. That is, for p prime, q = p(r) and an elliptic curve E : y(2) = x(3) + ax + b, we show that... 
2010 Mathematics subject classification | primary 11G05 | secondary 11K38 | MATHEMATICS | ELLIPTIC-CURVES | AVERAGE | STATISTICS | FAMILIES | elliptic curves | Sato-Tate theorem | Mathematics - Number Theory
Journal Article
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 06/2019, Volume 2019, Issue 12, pp. 3768 - 3811
We study fluctuations in the distribution of families of p-th Fourier coefficients a(f)(p) of normalized holomorphic Hecke eigenforms f of weight k with... 
MATHEMATICS | ZETA-FUNCTIONS | STATISTICS | CURVES | ZEROS
Journal Article
Journal Article
Journal of Number Theory, ISSN 0022-314X, 01/2019, Volume 194, pp. 44 - 82
We derive new bounds for moments of the error in the Sato–Tate law over families of elliptic curves. Our estimates are stronger than those obtained in [4] and... 
Sato–Tate conjecture | Moments | Elliptic curves | Central Limit Theorem | Traces of Hecke operators | MATHEMATICS | Sato-Tate conjecture | AVERAGE | LANG-TROTTER | CONJECTURE
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2015, Volume 65, Issue 2, pp. 549 - 603
Journal Article
Advances in Mathematics, ISSN 0001-8708, 08/2015, Volume 281, pp. 1242 - 1273
Journal Article
Commentarii Mathematici Helvetici, ISSN 0010-2571, 2014, Volume 89, Issue 4, pp. 895 - 919
We consider statistical properties of Hecke eigenvalues $A_j(p, 1)$ for fixed $p$ as $\phi_j$ runs through a basis of Hecke–Maaß cusp forms for the group... 
Number theory | Sato-Tate law | Ramanujan conjecture | Kuznetsov formula | Density results | density results | MATHEMATICS | EIGENVALUES | POINCARE-SERIES | CUSP FORMS | SUMS
Journal Article
Clinical Genetics, ISSN 0009-9163, 02/2018, Volume 93, Issue 2, pp. 242 - 247
Journal Article
Endoscopy, ISSN 0013-726X, 02/2015, Volume 47, Issue 2, pp. 181 - 182
Journal Article
Current Opinion in Colloid & Interface Science, ISSN 1359-0294, 2011, Volume 16, Issue 5, pp. 357 - 358
Journal Article
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