On the Zeros of a Class of Dirichlet Series |
From inside the book
Results 1-3 of 14
Page 10
... constants and m , n are non - negative integers with 2m + qn x ( q - 2 ) , ( -1 ) ... constant . Then , if ≥ η , Rez0 and z - s has its principal value , 1 ' n + ... positive number > ; max ( , ) . Then we have [ 1.18 ] Σ S ann Σ an n 01 10.
... constants and m , n are non - negative integers with 2m + qn x ( q - 2 ) , ( -1 ) ... constant . Then , if ≥ η , Rez0 and z - s has its principal value , 1 ' n + ... positive number > ; max ( , ) . Then we have [ 1.18 ] Σ S ann Σ an n 01 10.
Page 36
... positive constant ( see Potter [ 2 ] ) . From this result one easily deduces that , in the case mentioned , M ( o , T ) is not uniformly bounded in the half - plane 。> h . m As to the proof of theorem 9 we remark that , using the func ...
... positive constant ( see Potter [ 2 ] ) . From this result one easily deduces that , in the case mentioned , M ( o , T ) is not uniformly bounded in the half - plane 。> h . m As to the proof of theorem 9 we remark that , using the func ...
Page 45
Cornelis Gerrit Lekkerkerker. with some constant Д not depending on 8 and 6. Hence ∞ . G ( o , t ) 2 dt < 2π А 8-20 ( h ... positive constant b , such that r ( s ) > b for s belonging to this rectangle . So we find a -a | 9 ( 0 + it ) | 45.
Cornelis Gerrit Lekkerkerker. with some constant Д not depending on 8 and 6. Hence ∞ . G ( o , t ) 2 dt < 2π А 8-20 ( h ... positive constant b , such that r ( s ) > b for s belonging to this rectangle . So we find a -a | 9 ( 0 + it ) | 45.
Contents
Introduction | 1 |
The number of zeros in a horizontal strip | 22 |
Some mean value theorems | 35 |
Copyright | |
2 other sections not shown
Common terms and phrases
² dt ² dy A₁ A₂ absolute convergence apply lemma arbitrary automorphic form chapter character mod q CLASS OF DIRICHLET class of functions conditions of theorem converges absolutely converges somewhere critical line cusp form deduce defined denote the number Dirichlet L-functions Dirichlet series Epstein zeta-functions estimate exists a positive finite order follows form of dimension form with signature Fourier function R(s functional equation Further G₂ Hecke Hence holds I₁ identically zero integral function interval Lekkerkerker mean value modular form modular group n(r₁ N₁(T No(T non-real zeros number of zeros O(log o₁ positive constant positive integer positive number possesses property principal value proof of theorem real coefficients real number relation represent an integral result Riemann hypothesis right half-plane satisfies sin² strip Suppose T₁ theorem 13 transformation valid y)-function μα Σαπ