A) Logarithmic continuation B) Meromorphic continuation C) Polynomial continuation D) Holomorphic continuation
A) No poles B) Two simple poles C) One simple pole D) Infinitely many poles
A) s = 0 B) s = 1/2 C) s = 1 D) s = -1
A) Class number formula B) Euler product formula C) Functional equation D) Discriminant formula
A) Invariants of the prime ideals and residues B) Real and complex places C) Gamma and beta factors D) Invariants of the unit group and class group
A) Riemann zeta function B) Gamma function C) Hecke L-function D) Dirichlet L-series
A) Richard Dedekind B) Erich Hecke C) Bernhard Riemann D) John Tate
A) Leonhard Euler B) John Tate C) Carl Friedrich Gauss D) Erich Hecke
A) 1 / s B) -s C) s - 1 D) 1 - s
A) Unit group of K B) Degree of K C) Discriminant of K D) Class number of K
A) Class number B) Number of complex places C) Discriminant of K D) Number of real places
A) Total number of embeddings B) Degree over Q C) Number of conjugate pairs of complex places D) Number of real places
A) 2 * r1 + r2 B) r1 + 2 * r2 C) r1 + r2 D) r1 * r2
A) (2 * pi)-s/2 * Gamma(s/2) B) pi-s * Gamma(s) C) (2 * pi)-s * Gamma(s) D) pi-s/2 * Gamma(s/2)
A) pi-s/2 * Gamma(s/2) B) (2 * pi)-s/2 * Gamma(s) C) (2 * pi)-s * Gamma(s) D) pi-s * Gamma(s/2)
A) Using Hecke characters alone B) Using the class number and unit group C) Using absolute discriminant, gamma factors, and zeta_K(s) D) Using only the Riemann zeta function
A) Lambda_K(s) = Lambda_K(1 - s) B) Lambda_K(s) = Lambda_K(s - 1) C) Lambda_K(s) = -Lambda_K(s) D) Lambda_K(s) = Lambda_K(-s)
A) Cancel poles of the gamma factors B) Create new poles in the complex plane C) Determine the class number D) Shift the critical line
A) Roots of the discriminant B) Common zeros of zeta_K and Lambda_K C) Values where s = 1 D) Poles of the gamma factors
A) 0 <= Re(s) <= 1/2 B) 1 <= Re(s) <= 2 C) 0 <= Re(s) <= 1 D) -1 <= Re(s) <= 0
A) Vertical line Re(s) = 1 B) Imaginary axis C) Critical line Re(s) = 1/2 D) Real line Re(s) = 0
A) Riemann zeta function B) Hecke L-function C) Dirichlet series D) Gamma function
A) Turns poles into zeroes B) Shifts the poles to the real line C) Removes the poles, producing an entire function D) Doubles the number of poles
A) To infinity B) To the imaginary axis C) To Re(s) = 1 D) To the real line
A) Xi_K(overline{s}) = -Xi_K(s) B) Xi_K(s) = Xi_K(1 - s) C) Xi_K(overline{s}) = Xi_K(s) D) Xi_K(overline{s}) = overline{Xi_K(s)}
A) As a differential equation B) As a finite sum C) As a matrix determinant D) As a Dirichlet series
A) Richard Dedekind B) Carl Friedrich Gauss C) Bernhard Riemann D) Peter Gustav Lejeune Dirichlet
A) A Dedekind ring B) A field of fractions C) A polynomial ring D) A Euclidean domain
A) Rational integers B) Principal ideals C) Quotient rings D) Prime ideals
A) Always one B) The square of the generator C) The non-negative integer generating the ideal D) Zero
A) Cauchy's bound B) Riemann's bound C) Minkowski's bound D) Dirichlet's bound
A) O(log x) B) O(xs) C) O(x) D) O(1)
A) It is additive B) It is constant C) It is multiplicative D) It is logarithmic
A) Absolutely convergent B) Asymptotically zero C) Divergent D) Conditionally convergent
A) r1 - r2 B) r2 C) r1 + r2 - 1 D) r1 + r2
A) r1 B) r2 C) r1 + r2 - 1 D) r1 + r2
A) Taylor B) Dedekind C) Riemann D) Siegel
A) Arithmetically equivalent B) Algebraically closed C) Isomorphic D) Conjugate fields
A) de Smit B) Artin C) Perlis D) Bosma
A) 1977 B) 2002 C) 1995 D) 1983
A) Spec L B) Spec Q C) Spec Z D) Spec O_K
A) The induced representation B) The regular representation C) The Galois representation D) The trivial representation
A) The alternating representation B) The standard representation C) The regular representation D) The trivial representation
A) Gal(M/K) B) Gal(M/L) C) Gal(L/K) D) Spec O_K
A) Artin reciprocity B) Quadratic reciprocity C) Aramata–Brauer theorem D) Selberg orthonormality
A) Trivial representations B) Quadratic representations C) Irreducible representations D) Reducible representations
A) A Jacobi symbol B) An entire function C) A prime number D) A Galois group
A) Dedekind conjecture B) Quadratic reciprocity law C) Aramata–Brauer theorem D) Artin reciprocity law
A) Selberg orthonormality conjecture B) Aramata–Brauer theorem C) Artin reciprocity D) Uchida and van der Waall theorem
A) The Artin conjecture B) The Dirichlet L-function formula C) The Riemann hypothesis D) The quadratic reciprocity law
A) The Selberg orthonormality conjecture B) The Riemann zeta conjecture C) The quadratic field conjecture D) The abelian extension conjecture
A) The functional equation B) Algebraic K-theory C) Bernoulli numbers D) The critical line
A) Imaginary numbers B) Positive even integers C) Zero and positive integers D) Negative odd integers
A) Imaginary numbers B) Transcendental numbers C) Negative integers D) Nonzero rational numbers
A) Stephen Lichtenbaum B) Riemann C) Bernoulli D) Siegel |