Results 51 to 60 of about 1,430,683 (165)
Diophantine equations in partitions [PDF]
Mathematics of Computation, 1984 Given positive integers r 1
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Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
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On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.
Alan Murat
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An exponential diophantine equation [PDF]
Bulletin of the Australian Mathematical Society, 2001 Let p be an odd prime with p > 3. In this paper we give all positive integer solutions (x, y, m, n) of the equation x2 + p2m = yn, gcd (x, y) = 1, n > 2 satisfying 2 | n of 2 ∤ n and p ≢ (−1)(p−1)/2(mod 4n.
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Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems
Annalen der Physik, Volume 538, Issue 7, July 2026.ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández +3 more
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On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
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The Exponential Diophantine Equation 4m2+1x+5m2-1y=(3m)z
Abstract and Applied Analysis, 2014 Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if m>90 and 3|m, then the equation 4m2+1x + 5m2-1y=(3m)z has ...
Juanli Su, Xiaoxue Li
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An elegant model of the geodesic flow on the modular surface
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Caroline Series' [The modular surface and continued fractions, J. Lond. Math. Soc. (2), 31, no. 1, (1985), 69–80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well‐chosen symbolic coding.
Pierre Arnoux, Thomas A. Schmidt
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, 2010 In the first chapter we have given some definations, theorems, lemmas on Elementary Number Theory. This brief discussion is useful for next discussion on the main topic.
Strnadová, Pavlína, Panda, Sagar
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