Titlebook: Analytic Number Theory and Diophantine Problems; Proceedings of a Con A. C. Adolphson,J. B. Conrey,R. I. Yager Conference proceedings 1987

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Introduction and Theoretical Motivation,In 1943, A. Selberg [15] Deduced From The Riemann Hypothesis (Rh) that . for X. ≤ δ ≤ X., X ≥ 2. Selberg was concerned with small values of δ and the constraint δ ≤ X. was imposed more for convenience than out of necessity. For Larger δ we have the following result.

neuron

https://doi.org/10.1007/978-3-642-33938-7In his famous Habilitationsschrift of 1854 on trigonometric series and integration theory, Riemann gave the following interesting example which shows his high ingenuity of analysis and arithmetic as well.

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联想

https://doi.org/10.1007/978-3-031-03910-2Let m ≥ 1. The k-th polygonal number of order m+2 is the sum of the first k terms of the arithmetic progression 1, 1+m, l+2m, l+3m,… The polygonal numbers of orders 3 and 4 are the triangular numbers and squares, respectively.

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影响深远

Technologien für die intelligente AutomationTwo basic questions concerning the Ramanujan τ-function concern the size and variation of these numbers:

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TERRA

Simple Zeros of the Zeta-Function of a Quadratic Number Field, II,Let K be a fixed quadratic extension of . and write ζ.(s) for the Dedekind zeta-function of K, where s = σ + it. It is wellknown, and easy to prove, that the number N.(T) of zeros of ζ.(s) in the region 0 < σ < 1, 0 < t ≤ T satisfies . as T → ∞. On the other hand, not much is known about the number of . that are simple.

Longitude

Pair Correlation of Zeros and Primes in Short Intervals,In 1943, A. Selberg [15] Deduced From The Riemann Hypothesis (Rh) that . for X. ≤ δ ≤ X., X ≥ 2. Selberg was concerned with small values of δ and the constraint δ ≤ X. was imposed more for convenience than out of necessity. For Larger δ we have the following result.