Raghavendra Bhat

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20242026

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math.NT2026

An Arithmetic Sum Associated with the Classical Theta Function

Bruce C. Berndt, Raghavendra N. Bhat, Jeffrey L. Meyer +2

The sum $S (h, k) := \sum_{j = 1}^{k - 1} (- 1)^{j + 1 + [hj / k]}$ appears in the modular transformation formulae of the classical theta function $ϑ_{3} (z)$ . The double sum $S(k) := \sum_{h…

math.NT2025

Twisted aughts of alternating involutions

Raghavendra N. Bhat, Cristian Cobeli, Shuta Iwai +2

Let $M (n)$ be the subgroup of $G L (n, Z)$ generated by the particular involutions that are identical to the identity, except for a single line where $- 1$ and $+ 1$ …

math.NT2024

Filtered rays over iterated absolute differences on layers of integers

Raghavendra N. Bhat, Cristian Cobeli, Alexandru Zaharescu

The dynamical system generated by the iterated calculation of the high order gaps between neighboring terms of a sequence of natural numbers is remarkable and only incidentally cha…

math.NT2024

Almost all primes are not needed in Ternary Goldbach

Debmalya Basak, Raghavendra N. Bhat, Anji Dong +1

The ternary Goldbach conjecture states that every odd number $m ⩾ 7$ can be written as the sum of three primes. We construct a set of primes $P$ defined by an expa…