Selberg conjecture

Author: eutd

August undefined, 2024

WebIn this paper, we reinterpret the Colmez conjecture on the Faltings height of $\text{CM}$ abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a $\text{CM}$ abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for $\text{CM ... WebSeveral conjectures in mathematics, such as the Selberg conjecture, are equivalent to saying that certain representations are not complementary. For examples see the representation theory of SL2 (R).

Selbergs Eigenvalue Conjecture - American …

WebIn mathematics, the Selberg conjecture, named after Atle Selberg, is a theorem about the density of zeros of the Riemann zeta function ζ (1/2 + it ). It is known that the function has infinitely many zeroes on this line in the complex plane: the point at issue is how densely they are clustered. Web3 From simple geodesics to Witten’s conjecture We begin with Mirzakhani’s work on simple geodesics. In the 1940s, Del-sarte, Huber and Selberg established the prime number theorem for hyper-bolic surfaces, which states that the number of (oriented, primitive) closed geodesics on X2M g with length Lsatis es ˇ(X;L) ˘ eL L: camouflage orthodontic treatment

(PDF) On Selberg’s Eigenvalue Conjecture - ResearchGate

Web3 The Chowla-Selberg formula4 4 Elliptic periods6 5 Colmez’s conjecture for the Faltings height8 6 Deligne’s motive9 7 A factor of the Fermat Jacobian11 8 A Hodge class14 1 Abstract In this expository paper, we review the formula of Chowla and Selberg for the periods of elliptic curves with complex multiplication, and discuss two methods of ... WebMay 11, 2024 · Alexander Dobner Newman's conjecture (proved by Rodgers and Tao in 2024) concerns a certain family of deformations of the Riemann xi function for which there exists an associated constant (called the de Bruijn-Newman constant) such that all the zeros of lie on the critical line if and only if . first security login

Remembering Atle Selberg, 1917–2007 - ams.org

Heegner Point Kolyvagin System and Iwasawa Main Conjecture

WebApr 20, 2024 · The Suita conjecture proved to be true for the hyperbolic case (see [ 1, 2, 5, 8 ]), and it might be interesting to generalize similar results to non -hyperbolic cases. In this article, for a once-punctured complex torus X τ, u : = X τ ∖ { u }, which is a typical potential-theoretically parabolic Riemann surface, we construct a so-called ... WebJan 15, 2024 · As a byproduct we also prove the equality in the Greenberg-Iwasawa main conjecture for certain Rankin-Selberg product (Theorem 1.7) under some local conditions, and an improvement of Skinner’s result on a converse of Gross-Zagier and Kolyvagin theorem (Corollary 1.11). Download to read the full article text References camouflage outdoorWebNUMERICAL COMPUTATIONS WITH THE TRACE FORMULA AND THE SELBERG EIGENVALUE CONJECTURE ANDREW R. BOOKER AND ANDREAS STROMBER GSSON Abstract. We verify the Selberg eigenvalue conject first security loan application

"WebOct 22, 2007 · The importance of the Selberg integral. It has been remarked that a fair measure of the impact of Atle Selberg's work is the number of mathematical terms which bear his name. One of these is the Selberg integral, an n-dimensional generalization of the Euler beta integral. We trace its sudden rise to prominence, initiated by a question to ... " - Selberg conjecture

Selberg conjecture

WebSelberg’s Eigenvalue Conjecture 1272 NOTICES OF THE AMS VOLUME 42, NUMBER 11 I n the late 1970s, when I was a student atStanford University, I attended a seminar run by … WebApr 1, 2024 · To back up his conjecture, Selberg also proved the following assertion: $$\ell_1 (N) \geq 3/16.$$. Selberg's approach was to relate this problem to a purely arithmetical …

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WebAssuming conjectures 1 and 2 below, L-functions of irreducible cuspidal automorphic representations that satisfy the Ramanujan conjecture are primitive. Selberg's conjectures. In (Selberg 1992), Selberg made conjectures concerning the functions in S: Conjecture 1: For all F in S, there is an integer n F such that WebSelberg conjecture (or as above, the Ramanujan conjecture) would follow from the following statement: Given 7r an irreducible cuspidal automorphic representation and/3 with Re(/3) …

WebSelberg showed that the eigenvalues are at least 3/16. In mathematics, Selberg's conjecture, also known as Selberg's eigenvalue conjecture, conjectured by Selberg , states that the … WebSELBERG’S ORTHOGONALITY CONJECTURE FOR AUTOMORPHIC L-FUNCTIONS JIANYA LIU1 AND YANGBO YE2 Abstract. Let ˇ and ˇ0 be automorphic irreducible unitary cuspidal …

WebAug 6, 2007 · It was conjectured in the 18th century but despite many efforts, no proof had been found around that time. Riemann came close to proving the result, but the theory of functions of a complex variable was not sufficiently … WebOct 24, 2013 · What's the best record toward Selberg's eigenvalue conjecture: a Maass form on $\Gamma_0(N)$ has eigenvalue greater than or equal to 1/4? Stack Exchange Network …

WebWe construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM …

WebOn Montgomery's pair correlation conjecture: a tale of three integrals. Tuesday, October 19: 11:00: Zoom: Eun Hye Lee (Stony Brook) Subconvexity of Shintani Zeta Functions: Tuesday, October 26: 11:00: Zoom: Micah Milinovich: ... On the Rankin-Selberg problem. Abstract: In this talk, I will introduce a method to solve the Rankin-Selberg problem ... camouflage outdoor carpetWebSelberg conjecture Let denote the upper half-plane, the group of integer matrices of determinant one and Following H. Maass [a9], let denote the space of bounded functions … camouflage outdoor fabricWebSelberg’s conjecture is the archimedean analogue of the “Ramanujan Conjectures” on the Fourier coefficients of Maass forms. For these, much progress has been made in … camouflage outdoor gearWebSelberg conjecture (or as above, the Ramanujan conjecture) would follow from the following statement: Given 11" an irreducible cuspidal automorphic representation and 13 with Re(j3) > 0, there is an even Dirichlet character such that L(j3, 11" ® X) =1= o. Such problems have been studied by many authors ([ShiJ, [R], [BR]). first security longview texasWebSep 1, 2024 · Selberg's orthogonality conjecture has a strong impact on the theory of L-functions. For instance, under Selberg's orthogonality conjecture, Conrey and Ghosh [9] … first security login missoula mtWebDec 1, 1993 · Selberg Sums: A New Perspective. S. Patterson. Mathematics. 2016. Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in 1940s. The original versions of these sums were introduced by R.J. Evans in 1981, and following an elegant…. Expand. camouflage outdoor growWebOct 30, 2024 · On Selberg’s eigenvalue conjecture for moduli spaces of abelian differentials. Part of: Lie groups Dynamical systems with hyperbolic behavior Discontinuous groups … camouflage outdoor security cameras