Shifted convolution sums for GL(3)×GL(2)$GL(3)\times GL(2)$ averaged over weighted sets
Mathematika, Volume 70, Issue 2, April 2024.Abstract Let A(1,m)$A(1,m)$ be the Fourier coefficients of an SL(3,Z)$SL(3,\mathbb {Z})$ Hecke–Maass cusp form F$F$ and λ(m)$\lambda (m)$ be those of an SL(2,Z)$SL(2,\mathbb {Z})$ Hecke holomorphic or Hecke–Maass cusp form g$g$. Let H⊂⟦−X1−ε,X1+ε⟧$\mathcal {H}\subset \llbracket -X^{1-\varepsilon },X^{1+\varepsilon }\rrbracket$ and {a(h)}h∈H⊂C$\lbrace a(
Wing Hong Leung
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Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$
Proceedings of the London Mathematical Society, Volume 128, Issue 3, March 2024.Abstract We obtain the exponent of distribution 1/2+1/30$1/2+1/30$ for the ternary divisor function d3$d_3$ to square‐free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath‐Brown and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with GL(2)$GL(2)$ coefficients obtained using the delta ...
Prahlad Sharma
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The Explicit Formula for the Chebyshev–Von Mangoldt Function and the Prime Representing Constant
The Prime Representing Constant infinitely generates prime numbers. We discovered how to compute the Prime Representing Constant using the Hadamard product expansion. We also modified the classical Riemann–von Mangoldt explicit formula. While mathematically equivalent to the classical formula, the cosine-phase form is novel in its computational and ...
Ricie D. Bulanhagui +1 more
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From Grafts to Human Bioengineered Vascularized Skin Substitutes. [PDF]
Int J Mol Sci, 2020 Oualla-Bachiri W +3 more
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Riemann's Zeta Function and Prime Numbers : an approximation using von Mangoldt's explicit formula
, 2023 Syftet med denna uppsats är att klargöra kopplingen mellan Riemanns zeta funktion och primtalen. Den är till stor del baserad på Riemanns manuskript från 1859, där han approximerar primtalsfunktionen med hjälp av zeta funktionens icke-triviala nollställen. Huvudresultatet i uppsatsen är von Mangoldts explicita formel, vilken är en modifierad version av
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Spectral Stability of the von Mangoldt Function and the Generalized Riemann Hypothesis
A rigorous inverse reconstruction of the von Mangoldt function from zeta zeros. We demonstrate that spectral stability is equivalent to the GRH and analyze "ghost oscillations" using high-precision numerics and Random Matrix Theory.
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Liouville function, von Mangoldt function and norm forms at random binary forms
39 ...
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Pair correlation and twin primes revisited. [PDF]
Proc Math Phys Eng Sci, 2016 Conrey B, Keating JP.
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Riemann hypothesis for period polynomials of modular forms. [PDF]
Proc Natl Acad Sci U S A, 2016 Jin S, Ma W, Ono K, Soundararajan K.
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CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIES
CONVOLUTIONS OF THE VON MANGOLDT FUNCTION AND RELATED DIRICHLET SERIESIn this paper, we first give a brief survey on the theory of meromorphic continuation and natural boundaries of multiple Dirichlet series. Then we consider the double Dirichlet series Φ2(s) defined by the convolution of logarithmic derivatives of the Riemann zeta-function.
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