arXiv subjects

Apoorva Panidapu

Publications and source records attributed to Apoorva Panidapu.

7 recordsLinked to original sources

arXiv2026

Privacy Without Remedy: An Assessment of Data Broker Compliance with California Privacy Law

California's consumer privacy law is widely deemed to be the most protected in the United States, one of the few to expressly regulate third party entities that buy and sell consumer data (data brokers). We offer the first empirical assessment of data broker compliance with the 2018 California Consumer Privacy Act (CCPA) and the 2023 Delete Act, which requires data brokers to register with the state and report consumer rights requests metrics annually. First, we demonstrate that only 9% of 522 registered data brokers were fully compliant with transparency requirements after the Delete Act took effect, although we do identify slight improvements over time. Second, we descriptively characterize wide heterogeneity across data brokers in the volume of consumer rights requests received, with many reporting none. We bring in external business data to explore correlates associated with this variation, a challenge given the general lack of opacity into broker business practices. Third, in an audit of a sample of 250 data brokers' consumers request processes, we find that 43% make it impossible for consumers to exercise all privacy rights and 64% introduce at least one design feature that creates substantial friction into the consumer request process. Last, we show how these deficiencies stem from the decentralization of compliance decisions to brokers themselves, enforcement limitations, and regulatory ambiguity. We articulate reforms that could improve consumer privacy, transparency in broker practices, and compliance with these laws.

cs.CY↗

arXiv2023

Tamagawa Products for Elliptic Curves Over Number Fields

In recent work, Griffin, Ono, and Tsai constructs an $L-$series to prove that the proportion of short Weierstrass elliptic curves over $\mathbb{Q}$ with trivial Tamagawa product is $0.5054\dots$ and that the average Tamagawa product is $1.8183\dots$. Following their work, we generalize their $L-$series over arbitrary number fields $K$ to be \[L_{\mathrm{Tam}}(K; s):=\sum_{m=1}^{\infty}\frac{P_{\mathrm{Tam}}(K; m)}{m^s},\] where $P_{\mathrm{Tam}}(K;m)$ is the proportion of short Weierstrass elliptic curves over $K$ with Tamagawa product $m$. We then construct Markov chains to compute the exact values of $P_{\mathrm{Tam}}(K;m)$ for all number fields $K$ and positive integers $m$. As a corollary, we also compute the average Tamagawa product $L_{\mathrm{Tam}}(K;-1)$. We then use these results to uniformly bound $P_{\mathrm{Tam}}(K;1)$ and $L_{\mathrm{Tam}}(K,-1)$ in terms of the degree of $K$. Finally, we show that there exist sequences of $K$ for which $P_{\mathrm{Tam}}(K;1)$ tends to $0$ and $L_{\mathrm{Tam}}(K;-1)$ to $\infty$, as well as sequences of $K$ for which $P_{\mathrm{Tam}}(K;1)$ and $L_{\mathrm{Tam}}(K;-1)$ tend to $1$.

math.NT↗

arXiv2022

Explicit Calculations for Sono's Multidimensional Sieve of $E_2$-Numbers

We derive explicit formulas for integrals of certain symmetric polynomials used in Keiju Sono's multidimensional sieve of $E_2$-numbers, i.e., integers which are products of two distinct primes. We use these computations to produce the currently best-known bounds for gaps between multiple $E_2$-numbers. For example, we show there are infinitely many occurrences of four $E_2$-numbers within a gap size of 94 unconditionally and within a gap size of 32 assuming the Elliott-Halberstam conjecture for primes and sifted $E_2$-numbers.

math.NT↗

arXiv2022

Short-interval sector problems for CM elliptic curves

Let $E/\mathbb{Q}$ be an elliptic curve that has complex multiplication (CM) by an imaginary quadratic field $K$. For a prime $p$, there exists $θ_p \in [0, π]$ such that $p+1-\#E(\mathbb{F}_p) = 2\sqrt{p} \cos θ_p$. Let $x>0$ be large, and let $I\subseteq[0,π]$ be a subinterval. We prove that if $δ>0$ and $θ>0$ are fixed numbers such that $δ+θ<\frac{5}{24}$, $x^{1-δ}\leq h\leq x$, and $|I|\geq x^{-θ}$, then \[ \frac{1}{h}\sum_{\substack{x < p \le x+h \\ θ_p \in I}}\log{p}\sim \frac{1}{2}\mathbf{1}_{\fracπ{2}\in I}+\frac{|I|}{2π}, \] where $\mathbf{1}_{\fracπ{2}\in I}$ equals 1 if $\fracπ{2}\in I$ and $0$ otherwise. We also discuss an extension of this result to the distribution of the Fourier coefficients of holomorphic cuspidal CM newforms.

math.NT↗

arXiv2021

Small Gaps Between Three Almost Primes and Almost Prime Powers

A positive integer is called an $E_j$-number if it is the product of $j$ distinct primes. We prove that there are infinitely many triples of $E_2$-numbers within a gap size of $32$ and infinitely many triples of $E_3$-numbers within a gap size of $15$. Assuming the Elliot-Halberstam conjecture for primes and $E_2$-numbers, we can improve these gaps to $12$ and $5$, respectively. We can obtain even smaller gaps for almost primes, almost prime powers, or integers having the same exponent pattern in the their prime factorizations. In particular, if $d(x)$ denotes the number of divisors of $x$, we prove that there are integers $a,b$ with $1\leq a < b \leq 9$ such that $d(x)=d(x+a)=d(x+b) = 192$ for infinitely many $x$. Assuming Elliot-Halberstam, we prove that there are integers $a,b$ with $1\leq a < b \leq 4$ such that $d(x)=d(x+a)=d(x+b) = 24$ for infinitely many $x$.

math.NT↗

arXiv2020

A Bombieri-Vinogradov Theorem for primes in short intervals and small sectors

Let $K$ be a finite Galois extension of $\mathbb{Q}$. We count primes in short intervals represented by the norm of a prime ideal of $K$ satisfying a small sector condition determined by Hecke characters. We also show that such primes are well-distributed in arithmetic progressions in the sense of Bombieri-Vinogradov. This extends previous work of Duke and Coleman.

math.NT↗

arXiv2020

Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II

This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erdős-Mirksy conjecture which states that there are infinitely many positive integers $x$ such that $d(x)=d(x+1)$ where $d(x)$ denotes the number of divisors of $x$. This conjecture was first proven by Heath-Brown in 1984, but the method did not reveal the nature of the set of values $d(x)$ for such $x$. In particular, one could not conclude that there was any particular value $A$ for which $d(x)=d(x+1)=A$ infinitely often. In the previous paper arXiv:0803.2636, the authors showed that there are infinitely many positive integers $x$ such that both $x$ and $x+1$ have exponent pattern $\{2,1,1,1\}$, so $d(x)=d(x+1)=24$. Similar results were known for certain shifts $n$, i.e., $x$ and $x+n$ have the same fixed exponent pattern infinitely often. This was done for shifts $n$ which are either even or not divisible by the product of a pair of twin primes. The goal of this paper is to give simple proofs of results on exponent patterns for an arbitrary shift $n$.

math.NT↗