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Journal of Number Theory, ISSN 0022-314X, 11/2017, Volume 180, pp. 219 - 233
For two positive definite integral ternary quadratic forms f and g and a positive integer n, if n⋅g is represented by f and n⋅dg=df, then the pair (f,g) is... 
Genus-correspondence | Spinor genus | MATHEMATICS | REPRESENTATIONS | TERNARY QUADRATIC-FORMS
Journal Article
ACTA ARITHMETICA, ISSN 0065-1036, 2019, Volume 191, Issue 3, pp. 259 - 287
Journal Article
Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 2, pp. 535 - 548
Let m be a positive integer satisfying m equivalent to 1 (mod 4) and (m/7) = 1. Then there exist integers x, y, epsilon Z such that m = x(2) + 7y(2) + 49z(2).... 
MATHEMATICS | SPINOR GENERA
Journal Article
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0065-9266, 07/2008, Volume 194, Issue 907, pp. 1 - 1
The purpose of this paper is to establish the spinor genus theory of quadratic forms over global function fields in characteristic 2. The first part of the... 
MATHEMATICS | spinor genus | DYADIC LOCAL-FIELDS | integral lattice | spinor norm | REPRESENTATIONS | genus | INTEGRAL ORTHOGONAL GROUPS | QUADRATIC-FORMS | integral orthogonal group | class
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 1/2016, Volume 39, Issue 1, pp. 179 - 199
In this paper, we show that half of non-zero coefficients of the spinor zeta function of a Siegel cusp form of genus 2 are positive and half are negative. We... 
11F46 | 11M41 | Functions of a Complex Variable | 11N56 | Field Theory and Polynomials | Mathematics | 11F30 | Fourier coefficients | Fourier Analysis | Siegel form | Spinor zeta function | Number Theory | 11N37 | Combinatorics | Hecke eigenvalues
Journal Article
Compositio Mathematica, ISSN 0010-437X, 3/2004, Volume 140, Issue 2, pp. 287 - 300
We determine exactly when a quadratic form is represented by a spinor genus of another quadratic form of three or four variables. We apply this to extend the... 
Spinor genera | Hardy-Littlewood varieties | Representation mass | spinor genera | MATHEMATICS | FIELDS | HOMOGENEOUS VARIETIES | INTEGERS | representation mass | POINTS | TERNARY QUADRATIC-FORMS
Journal Article
RAMANUJAN JOURNAL, ISSN 1382-4090, 01/2016, Volume 39, Issue 1, pp. 179 - 199
In this paper, we show that half of non-zero coefficients of the spinor zeta function of a Siegel cusp form of genus 2 are positive and half are negative. We... 
MATHEMATICS | Siegel form | REPRESENTATIONS | MULTIPLICATIVE FUNCTIONS | Spinor zeta function | COEFFICIENTS | Hecke eigenvalues | Fourier coefficients | SHORT INTERVALS | MODULAR-FORMS
Journal Article
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, ISSN 0025-5858, 4/2013, Volume 83, Issue 1, pp. 29 - 52
We prove the functional equation for the twisted spinor L-series of a cuspidal, holomorphic Siegel eigenform for the full modular group of genus 2. It follows... 
Fourier-Jacobi expansion | 11F46 | Spinor zeta-function | 11F50 | Mathematics | Siegel modular forms | Paramodular group | Topology | 11F66 | Geometry | Algebra | Number Theory | Differential Geometry | Combinatorics | Rankin convolution | FORMS | MATHEMATICS | DIRICHLET SERIES
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 03/2014, Volume 10, Issue 2, pp. 327 - 339
In this paper, we establish a Voronoi formula for the spinor zeta function of a Siegel cusp form of genus 2. We deduce from this formula quantitative results... 
Spinor zeta function | Voronoi formula | Siegel form | Fourier coefficients | MATHEMATICS | NEGATIVE HECKE EIGENVALUE | Mathematics | Number Theory
Journal Article
Asian Journal of Mathematics, ISSN 1093-6106, 2007, Volume 11, Issue 3, pp. 427 - 458
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 12/2011, Volume 26, Issue 3, pp. 407 - 417
Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp 2(ℤ) of genus 2. The Fourier coefficients of the spinor zeta function Z F (s)... 
Riesz mean | 11F46 | Fourier Analysis | Functions of a Complex Variable | Field Theory and Polynomials | Spinor zeta function | Mathematics | Number Theory | Combinatorics | MATHEMATICS
Journal Article
Proyecciones, ISSN 0716-0917, 2017, Volume 36, Issue 1, pp. 131 - 148
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 09/2018, Volume 14, Issue 8, pp. 2239 - 2256
For each integer m ≥ 3 , let P m ( x ) denote the generalized m -gonal number ( m − 2 ) x 2 − ( m − 4 ) x 2 with x ∈ ℤ . Given positive integers a , b , c , k... 
Spinor exceptions | Polygonal numbers | Ternary quadratic forms | MATHEMATICS | TRIANGULAR NUMBERS | INTEGERS | spinor exceptions | REPRESENTATION | SPINOR GENERA | ternary quadratic forms | TERNARY QUADRATIC-FORMS
Journal Article
Journal of Number Theory, ISSN 0022-314X, 11/2015, Volume 156, pp. 247 - 262
An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers.... 
Primitive spinor exceptions | Ternary quadratic forms | FORMS | MATHEMATICS | REPRESENTATIONS | INTEGERS | NORMS | SPINOR GENERA | LOCAL INTEGRAL ROTATIONS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 8/2017, Volume 368, Issue 3, pp. 923 - 943
Let $$-d$$ - d be a a negative discriminant and let T vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms... 
11F46 | Primary 11E12 | Mathematics, general | Secondary 11F27 | Mathematics | 11F30 | 11E45 | THETA-SERIES | MATHEMATICS | QUATERNION ALGEBRAS | SPINOR GENERA | TWISTED L-FUNCTIONS | EISENSTEIN SERIES | Mathematics - Number Theory
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2012, Volume 62, Issue 2, pp. 807 - 819
A representation field for a non-maximal order h in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set... 
Spinor genera | Spinor class fields | Maximal orders | Central simple algebras | spinor genera | MATHEMATICS | maximal orders | central simple algebras | spinor class fields
Journal Article
by Kim, EC
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, ISSN 0926-2245, 06/2007, Volume 25, Issue 3, pp. 309 - 321
It is well known [M.F. Atiyah, V.K. Patodi, I.M. Singer, Spectral asymmetry and Riemannian geometry 1, Math. Proc. Camb. Phil. Soc. 77 (1975) 43-69] that the... 
MATHEMATICS | MATHEMATICS, APPLIED | OPERATOR | spectrum | symmetry | CURVATURE | HARMONIC SPINORS | Dirac operator
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2014, Volume 141, pp. 202 - 213
An integral quadratic polynomial (with positive definite quadratic part) is called almost universal if it represents all but finitely many positive integers.... 
Primitive spinor exceptions | Ternary quadratic forms | FORMS | MATHEMATICS | TRIANGULAR NUMBERS | REPRESENTATIONS | INTEGERS | NORMS | SPINOR GENERA | SQUARES | LOCAL INTEGRAL ROTATIONS | MIXED SUMS
Journal Article
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