Author

K. S. Raghava

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Preprint Oct 2026

Logarithmic moments of the Rogers Ramanujan continued fraction and odd zeta values

We study how the two cusp expansions of the Rogers-Ramanujan continued fraction control its ordinary and logarithmic Mellin moments. Ramanujan's factorizations express the logarithmic transform as a combination of products of zeta and quadratic Dirichlet $L$-functions. Its adjacent integer and half-integer values give...

K. S. Raghava · 0 citations

Preprint Sep 2026

Arithmetic Constraints and Limit Laws for Diagonal Rational Partitions

Let $R_N(m)$ count unordered partitions of $m$ into reduced positive fractions whose numerators and denominators are at most $N$, excluding integer parts. Uniformly for $\rho$ in compact positive intervals, $\log R_N(\lfloor\rho N\rfloor)=\sqrt{2\rho}\,N^{3/2}-\kappa(\rho)N^{3/2}/\log N+o(N^{3/2}/\log N)$. The positive...

K. S. Raghava · 0 citations

Preprint Sep 2026

Root-of-Unity Sections of Dilated Euler-Product Quotients

We study root-of-unity sections of quotients formed from dilated Euler products. At the boundary point $q=1$, odd sections tend to nonzero cyclotomic constants, whereas even sections have infinitely many simple real poles. We determine the locations, spacing, and residues of all sufficiently late poles. In the cubic...

K. S. Raghava · 0 citations